diff --git a/AABB_tree/demo/AABB_tree/Scene.cpp b/AABB_tree/demo/AABB_tree/Scene.cpp
index a84d9d3f2542..b7bb10f80c80 100644
--- a/AABB_tree/demo/AABB_tree/Scene.cpp
+++ b/AABB_tree/demo/AABB_tree/Scene.cpp
@@ -1252,9 +1252,7 @@ void Scene::cutting_plane(bool override)
             return;
         }
 
-        // Should not be here
-        std::cerr << "Unknown cut_plane type" << std::endl;
-        CGAL_assertion(false);
+        CGAL_unreachable();
     }
 }
 
diff --git a/Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Algebraic_curve_kernel_2.h b/Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Algebraic_curve_kernel_2.h
index c3be1d699544..409087417e56 100644
--- a/Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Algebraic_curve_kernel_2.h
+++ b/Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Algebraic_curve_kernel_2.h
@@ -1665,13 +1665,8 @@ class Algebraic_curve_kernel_2 : public AlgebraicKernel_d_1{
             const Polynomial_2& f = ca1.polynomial_2();
             const Polynomial_2& g = ca2.polynomial_2();
 
-            if(f == g) {
-              // both curves are equal, but have different representations!
-              // std::cout <<"f: " << f <<std::endl;
-              // std::cout <<"g: " << g <<std::endl;
-              CGAL_assertion(false);
-              return false;
-            }
+            CGAL_assertion_msg(f != g, "both curves are equal, but have different representations!");
+
             Gcd_cache_2& gcd_cache = _m_kernel->gcd_cache_2();
             typedef typename Curve_analysis_2::size_type size_type;
             Polynomial_2 gcd = gcd_cache(std::make_pair(f,g));
diff --git a/Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Curve_analysis_2.h b/Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Curve_analysis_2.h
index 6fecb592a121..9e46877c7d5f 100644
--- a/Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Curve_analysis_2.h
+++ b/Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Curve_analysis_2.h
@@ -890,7 +890,7 @@ class Curve_analysis_2 : public ::CGAL::Handle_with_policy< Rep_ > {
                 break;
             }
             default:{
-              CGAL_assertion(false); // !!! Never reached
+              CGAL_unreachable();
             }
             }
         }
diff --git a/Alpha_shapes_2/include/CGAL/Alpha_shapes_2/internal/Lazy_alpha_nt_2.h b/Alpha_shapes_2/include/CGAL/Alpha_shapes_2/internal/Lazy_alpha_nt_2.h
index 6d77e38f9045..fb2b69ce0737 100644
--- a/Alpha_shapes_2/include/CGAL/Alpha_shapes_2/internal/Lazy_alpha_nt_2.h
+++ b/Alpha_shapes_2/include/CGAL/Alpha_shapes_2/internal/Lazy_alpha_nt_2.h
@@ -212,7 +212,7 @@ class Lazy_alpha_nt_2
         exact_ = Exact_squared_radius()( to_exact(*data().p0),to_exact(*data().p1),to_exact(*data().p2) );
         break;
       default:
-        CGAL_assertion(false);
+        CGAL_unreachable();
     }
   }
 
@@ -229,7 +229,7 @@ class Lazy_alpha_nt_2
         approx_ = Approx_squared_radius()( to_approx(*data().p0),to_approx(*data().p1),to_approx(*data().p2) );
         break;
       default:
-        CGAL_assertion(false);
+        CGAL_unreachable();
     }
   }
 
diff --git a/Alpha_shapes_3/include/CGAL/Alpha_shapes_3/internal/Lazy_alpha_nt_3.h b/Alpha_shapes_3/include/CGAL/Alpha_shapes_3/internal/Lazy_alpha_nt_3.h
index 219c307815a1..2603c6af7849 100644
--- a/Alpha_shapes_3/include/CGAL/Alpha_shapes_3/internal/Lazy_alpha_nt_3.h
+++ b/Alpha_shapes_3/include/CGAL/Alpha_shapes_3/internal/Lazy_alpha_nt_3.h
@@ -205,7 +205,7 @@ class Lazy_alpha_nt_3{
         exact_ = Exact_squared_radius()( to_exact(*data().p0),to_exact(*data().p1),to_exact(*data().p2),to_exact(*data().p3) );
       break;
       default:
-        CGAL_assertion(false);
+        CGAL_unreachable();
     }
   }
 
@@ -224,7 +224,7 @@ class Lazy_alpha_nt_3{
         approx_ = Approx_squared_radius()( to_approx(*data().p0),to_approx(*data().p1),to_approx(*data().p2),to_approx(*data().p3) );
       break;
       default:
-        CGAL_assertion(false);
+        CGAL_unreachable();
     }
   }
 
diff --git a/Arrangement_on_surface_2/include/CGAL/Arr_point_location/Td_X_trapezoid.h b/Arrangement_on_surface_2/include/CGAL/Arr_point_location/Td_X_trapezoid.h
index 9904b1705420..674db5583fe0 100644
--- a/Arrangement_on_surface_2/include/CGAL/Arr_point_location/Td_X_trapezoid.h
+++ b/Arrangement_on_surface_2/include/CGAL/Arr_point_location/Td_X_trapezoid.h
@@ -605,10 +605,9 @@ class Td_X_trapezoid : public Handle
     case CGAL_TD_VERTEX:
       return TD_VERTEX;
     default:
-       CGAL_assertion(false);
-       return TD_TRAPEZOID;
-    }
+       CGAL_unreachable();
     }
+  }
 
   /*! Access trapezoid type flag. */
   CGAL_TD_INLINE unsigned char type_flag() const
diff --git a/BGL/include/CGAL/boost/graph/internal/initialized_index_maps_helpers.h b/BGL/include/CGAL/boost/graph/internal/initialized_index_maps_helpers.h
index eddefcec7fb2..7a3320fc97fd 100644
--- a/BGL/include/CGAL/boost/graph/internal/initialized_index_maps_helpers.h
+++ b/BGL/include/CGAL/boost/graph/internal/initialized_index_maps_helpers.h
@@ -80,13 +80,6 @@ bool is_index_map_valid(const CGAL::internal_np::face_index_t, FaceIndexProperty
   return is_index_map_valid(face_index_map, num_faces(g), faces(g));
 }
 
-template <typename PropertyTag, typename IndexPropertyMap, typename Graph>
-void initialize_index_map(const PropertyTag, IndexPropertyMap, const Graph&)
-{
-  // Unknown parameter; should never be here.
-  CGAL_assertion(false);
-}
-
 template <typename IndexPropertyMap,
           typename Graph,
           bool is_writable = CGAL::internal::Is_writable_property_map<IndexPropertyMap>::value>
@@ -120,12 +113,6 @@ struct Index_map_initializer
       put(face_index_map, fd, i++);
   }
 
-  template <typename PropertyTag>
-  void operator()(const PropertyTag, IndexPropertyMap, const Graph&)
-  {
-    // Unknown parameter; should never be here.
-    CGAL_assertion(false);
-  }
 };
 
 template <typename IndexPropertyMap, typename Graph>
diff --git a/Classification/include/CGAL/Classification/Image.h b/Classification/include/CGAL/Classification/Image.h
index 084e9572764a..afdee2d6e2a4 100644
--- a/Classification/include/CGAL/Classification/Image.h
+++ b/Classification/include/CGAL/Classification/Image.h
@@ -46,7 +46,7 @@ class Image
   // https://github.com/boostorg/core/issues/148
   Image(const Image&)
   {
-      CGAL_assertion(false);
+      CGAL_unreachable();
   }
 
   Image () : m_width(0), m_height(0), m_depth(0)
diff --git a/Combinatorial_map/include/CGAL/Combinatorial_map_storages_with_index.h b/Combinatorial_map/include/CGAL/Combinatorial_map_storages_with_index.h
index d69147d18206..2966bf0b9d53 100644
--- a/Combinatorial_map/include/CGAL/Combinatorial_map_storages_with_index.h
+++ b/Combinatorial_map/include/CGAL/Combinatorial_map_storages_with_index.h
@@ -169,13 +169,8 @@ namespace CGAL {
     {
       // Allocate a dart for null_dart_descriptor
       assert(mdarts.empty()); // the compact container is empty
-      Dart_index local_null_dart_descriptor = mdarts.emplace();
-      if(local_null_dart_descriptor!=0)
-      {
-        std::cerr<<"[ERROR] fatal in Combinatorial_map_storage_with_index::init_storage"
-                 <<std::endl;
-        CGAL_assertion(false);
-      }
+      CGAL_assertion_code( Dart_index local_null_dart_descriptor = ) mdarts.emplace();
+      CGAL_assertion_msg(local_null_dart_descriptor ==0, "[ERROR] fatal in Combinatorial_map_storage_with_index::init_storage");
     }
 
     void clear_storage()
diff --git a/Cone_spanners_2/include/CGAL/Compute_cone_boundaries_2.h b/Cone_spanners_2/include/CGAL/Compute_cone_boundaries_2.h
index 4256fd0dc179..f1e83b22b0ba 100644
--- a/Cone_spanners_2/include/CGAL/Compute_cone_boundaries_2.h
+++ b/Cone_spanners_2/include/CGAL/Compute_cone_boundaries_2.h
@@ -91,10 +91,8 @@ class Compute_cone_boundaries_2 {
     DirectionOutputIterator operator()(const unsigned int cone_number,
                                        const Direction_2& initial_direction,
                                        DirectionOutputIterator result)  {
-        if (cone_number<2) {
-            std::cout << "The number of cones must be larger than 1!" << std::endl;
-            CGAL_assertion(false);
-        }
+
+        CGAL_assertion_msg(cone_number>1, "The number of cones must be larger than 1");
 
         *result++ = initial_direction;
 
diff --git a/Cone_spanners_2/include/CGAL/Construct_theta_graph_2.h b/Cone_spanners_2/include/CGAL/Construct_theta_graph_2.h
index d4b47ed33c22..d36a7068f141 100644
--- a/Cone_spanners_2/include/CGAL/Construct_theta_graph_2.h
+++ b/Cone_spanners_2/include/CGAL/Construct_theta_graph_2.h
@@ -99,10 +99,7 @@ class Construct_theta_graph_2 {
                             ): cone_number(k), cones_choice(cones_selected), rays(std::vector<Direction_2>(k))
 
     {
-        if (k<2) {
-            std::cout << "The number of cones must be larger than 1!" << std::endl;
-            CGAL_assertion(false);
-        }
+        CGAL_assertion_msg(k>1, "The number of cones must be larger than 1");
 
         /* Initialize a functor, specialization will happen here depending on the kernel type to
          compute the cone boundaries either exactly or inexactly */
diff --git a/Cone_spanners_2/include/CGAL/Construct_yao_graph_2.h b/Cone_spanners_2/include/CGAL/Construct_yao_graph_2.h
index 8f2b599f311a..71b4f338dd4b 100644
--- a/Cone_spanners_2/include/CGAL/Construct_yao_graph_2.h
+++ b/Cone_spanners_2/include/CGAL/Construct_yao_graph_2.h
@@ -93,10 +93,7 @@ class Construct_yao_graph_2 {
                           ): cone_number(k), cones_choice(cones_selected), rays(std::vector<Direction_2>(k))
 
     {
-        if (k<2) {
-            std::cout << "The number of cones must be larger than 1!" << std::endl;
-            CGAL_assertion(false);
-        }
+        CGAL_assertion_msg(k>1, "The number of cones must be larger than 1");
 
         /* Initialize a functor, specialization will happen here depending on the kernel type to
          compute the cone boundaries either exactly or inexactly */
diff --git a/Homogeneous_kernel/include/CGAL/Homogeneous/Aff_transformationH2.h b/Homogeneous_kernel/include/CGAL/Homogeneous/Aff_transformationH2.h
index 7678de819f53..b4c0daf7a5e9 100644
--- a/Homogeneous_kernel/include/CGAL/Homogeneous/Aff_transformationH2.h
+++ b/Homogeneous_kernel/include/CGAL/Homogeneous/Aff_transformationH2.h
@@ -876,7 +876,6 @@ Aff_transformation_repH2<R>::homogeneous(int i, int j) const
             }
   }
   CGAL_unreachable();
-  return RT(0);
 }
 
 template < class R >
@@ -920,7 +919,6 @@ Translation_repH2<R>::homogeneous(int i, int j) const
             }
   }
   CGAL_unreachable();
-  return RT(0);
 }
 
 template < class R >
@@ -955,7 +953,6 @@ Translation_repH2<R>::cartesian(int i, int j) const
             }
   }
   CGAL_unreachable();
-  return FT(0);
 }
 
 template < class R >
@@ -991,7 +988,6 @@ homogeneous(int i, int j) const
             }
   }
   CGAL_unreachable();
-  return RT(0);
 }
 
 template < class R >
@@ -1027,7 +1023,6 @@ cartesian(int i, int j) const
             }
   }
   CGAL_unreachable();
-  return FT(0);
 }
 
 template < class R >
@@ -1063,7 +1058,6 @@ homogeneous(int i, int j) const
             }
   }
   CGAL_unreachable();
-  return RT(0);
 }
 
 template <class R>
@@ -1099,7 +1093,6 @@ cartesian(int i, int j) const
             }
   }
   CGAL_unreachable();
-  return FT(0);
 }
 
 template < class R >
@@ -1136,7 +1129,6 @@ homogeneous(int i, int j) const
             }
   }
   CGAL_unreachable();
-  return RT(0);
 }
 
 template <class R>
@@ -1173,7 +1165,6 @@ cartesian(int i, int j) const
             }
   }
   CGAL_unreachable();
-  return FT(0);
 }
 
 } //namespace CGAL
diff --git a/Homogeneous_kernel/include/CGAL/Homogeneous/Aff_transformationH3.h b/Homogeneous_kernel/include/CGAL/Homogeneous/Aff_transformationH3.h
index fa0ba377b4d3..23d72aa4034a 100644
--- a/Homogeneous_kernel/include/CGAL/Homogeneous/Aff_transformationH3.h
+++ b/Homogeneous_kernel/include/CGAL/Homogeneous/Aff_transformationH3.h
@@ -737,7 +737,6 @@ homogeneous(int i, int j) const
             }
   }
   CGAL_unreachable();
-  return RT0;
 }
 
 template < class R >
@@ -895,7 +894,6 @@ Translation_repH3<R>::homogeneous(int i, int j) const
             }
   }
   CGAL_unreachable();
-  return RT0;
 }
 
 template < class R >
diff --git a/Intersections_2/include/CGAL/Intersections_2/Ray_2_Ray_2.h b/Intersections_2/include/CGAL/Intersections_2/Ray_2_Ray_2.h
index 850f3e364b07..9f020e5cb27b 100644
--- a/Intersections_2/include/CGAL/Intersections_2/Ray_2_Ray_2.h
+++ b/Intersections_2/include/CGAL/Intersections_2/Ray_2_Ray_2.h
@@ -22,6 +22,7 @@
 #include <CGAL/Segment_2.h>
 #include <CGAL/Point_2.h>
 #include <CGAL/kernel_assertions.h>
+#include <CGAL/assertions.h>
 #include <CGAL/number_utils.h>
 #include <CGAL/Intersections_2/Line_2_Line_2.h>
 #include <CGAL/Intersection_traits_2.h>
@@ -185,8 +186,7 @@ Ray_2_Ray_2_pair<K>::intersection_type() const
         }
         }
     default:
-        CGAL_kernel_assertion(false); // should not be reached:
-        return _result;
+        CGAL_unreachable();
     }
 }
 
diff --git a/Intersections_2/include/CGAL/Intersections_2/Ray_2_Segment_2.h b/Intersections_2/include/CGAL/Intersections_2/Ray_2_Segment_2.h
index acc6d4a41dfa..2ab57031e30b 100644
--- a/Intersections_2/include/CGAL/Intersections_2/Ray_2_Segment_2.h
+++ b/Intersections_2/include/CGAL/Intersections_2/Ray_2_Segment_2.h
@@ -23,6 +23,7 @@
 #include <CGAL/Point_2.h>
 #include <CGAL/Line_2.h>
 #include <CGAL/kernel_assertions.h>
+#include <CGAL/assertions.h>
 #include <CGAL/number_utils.h>
 #include <CGAL/Intersections_2/Line_2_Line_2.h>
 #include <CGAL/Intersection_traits_2.h>
@@ -203,8 +204,7 @@ Ray_2_Segment_2_pair<K>::intersection_type() const
         }
         }
     default:
-        CGAL_kernel_assertion(false); // should not be reached:
-        return _result;
+        CGAL_unreachable();
     }
 
 }
diff --git a/Intersections_2/include/CGAL/Intersections_2/Segment_2_Segment_2.h b/Intersections_2/include/CGAL/Intersections_2/Segment_2_Segment_2.h
index 28d7920bd2a9..064496e39296 100644
--- a/Intersections_2/include/CGAL/Intersections_2/Segment_2_Segment_2.h
+++ b/Intersections_2/include/CGAL/Intersections_2/Segment_2_Segment_2.h
@@ -21,6 +21,7 @@
 #include <CGAL/Segment_2.h>
 #include <CGAL/Point_2.h>
 #include <CGAL/kernel_assertions.h>
+#include <CGAL/assertions.h>
 #include <CGAL/number_utils.h>
 #include <CGAL/predicates_on_points_2.h>
 #include <CGAL/Line_2.h>
@@ -141,8 +142,7 @@ seg_seg_do_intersect_crossing(
     default:
       CGAL_unreachable();
     }
-    CGAL_kernel_assertion(false);
-    return S2S2_inter_info(false);
+    CGAL_unreachable();
 }
 
 // used internally by Arr_segment_traits_2template <class K>
@@ -202,8 +202,7 @@ seg_seg_do_intersect_contained(
     default:
       CGAL_unreachable();
     }
-    CGAL_kernel_assertion(false);
-    return S2S2_inter_info(false);
+    CGAL_unreachable();
 }
 
 // used internally by Arr_segment_traits_2
@@ -319,8 +318,7 @@ do_intersect_with_info(const typename K::Segment_2 &seg1,
       CGAL_unreachable();
     }
 
-    CGAL_kernel_assertion(false);
-    return S2S2_inter_info(false);
+    CGAL_unreachable();
 }
 
 
diff --git a/Intersections_3/include/CGAL/Intersections_3/internal/Line_3_Triangle_3_do_intersect.h b/Intersections_3/include/CGAL/Intersections_3/internal/Line_3_Triangle_3_do_intersect.h
index a5b5dd1fc76b..5f127755af2c 100644
--- a/Intersections_3/include/CGAL/Intersections_3/internal/Line_3_Triangle_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/Intersections_3/internal/Line_3_Triangle_3_do_intersect.h
@@ -15,6 +15,7 @@
 
 #include <CGAL/enum.h>
 #include <CGAL/kernel_assertions.h>
+#include <CGAL/assertions.h>
 
 namespace CGAL {
 namespace Intersections {
@@ -57,13 +58,11 @@ do_intersect(const typename K::Triangle_3& t,
           case POSITIVE: return (orientation(p,q,c,a) != NEGATIVE);
           case NEGATIVE: return (orientation(p,q,c,a) != POSITIVE);
           case COPLANAR: return true;
-          default: // should not happen.
-            CGAL_kernel_assertion(false);
-            return false;
+          default:
+            CGAL_unreachable();
         }
-      default: // should not happen.
-        CGAL_kernel_assertion(false);
-        return false;
+      default:
+        CGAL_unreachable();
     }
   }
 
diff --git a/Intersections_3/include/CGAL/Intersections_3/internal/Plane_3_Triangle_3_do_intersect.h b/Intersections_3/include/CGAL/Intersections_3/internal/Plane_3_Triangle_3_do_intersect.h
index ea0462dadd6e..952211f0c412 100644
--- a/Intersections_3/include/CGAL/Intersections_3/internal/Plane_3_Triangle_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/Intersections_3/internal/Plane_3_Triangle_3_do_intersect.h
@@ -15,6 +15,7 @@
 
 #include <CGAL/enum.h>
 #include <CGAL/kernel_assertions.h>
+#include <CGAL/assertions.h>
 
 namespace CGAL {
 namespace Intersections {
@@ -43,8 +44,7 @@ do_intersect(const typename K::Triangle_3& t,
   case ON_ORIENTED_BOUNDARY:
     return true;
   default:// should not happen.
-    CGAL_kernel_assertion(false);
-    return false;
+    CGAL_unreachable();
   }
 }
 
diff --git a/Intersections_3/include/CGAL/Intersections_3/internal/Point_3_Triangle_3_do_intersect.h b/Intersections_3/include/CGAL/Intersections_3/internal/Point_3_Triangle_3_do_intersect.h
index f22d551e8421..c2429b68fc98 100644
--- a/Intersections_3/include/CGAL/Intersections_3/internal/Point_3_Triangle_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/Intersections_3/internal/Point_3_Triangle_3_do_intersect.h
@@ -15,6 +15,7 @@
 
 #include <CGAL/enum.h>
 #include <CGAL/kernel_assertions.h>
+#include <CGAL/assertions.h>
 
 namespace CGAL {
 namespace Intersections {
@@ -59,12 +60,10 @@ do_intersect(const typename K::Triangle_3& t,
       return (coplanar_orientation(c,a,p) != POSITIVE);
     case COLLINEAR: return true;
     default: // should not happen.
-      CGAL_kernel_assertion(false);
-      return false;
+      CGAL_unreachable();
     }
   default: // should not happen.
-    CGAL_kernel_assertion(false);
-    return false;
+    CGAL_unreachable();
   }
 }
 
diff --git a/Intersections_3/include/CGAL/Intersections_3/internal/Ray_3_Triangle_3_do_intersect.h b/Intersections_3/include/CGAL/Intersections_3/internal/Ray_3_Triangle_3_do_intersect.h
index ada4bc5207eb..c429172b3c56 100644
--- a/Intersections_3/include/CGAL/Intersections_3/internal/Ray_3_Triangle_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/Intersections_3/internal/Ray_3_Triangle_3_do_intersect.h
@@ -15,6 +15,7 @@
 
 #include <CGAL/enum.h>
 #include <CGAL/kernel_assertions.h>
+#include <CGAL/assertions.h>
 
 namespace CGAL {
 namespace Intersections {
@@ -139,9 +140,8 @@ do_intersect_coplanar(const typename K::Triangle_3& t,
       // a is isolated on the positive side
       return visitor.result(coplanar_orientation(*a,*c,p) != POSITIVE);
 
-    default: // should not happen.
-      CGAL_kernel_assertion(false);
-      return visitor.result(false);
+    default:
+      CGAL_unreachable();
     }
 
   case NEGATIVE:
@@ -165,9 +165,8 @@ do_intersect_coplanar(const typename K::Triangle_3& t,
       // a is isolated on the negative side
       return visitor.result(coplanar_orientation(*b,*a,p) != POSITIVE);
 
-    default: // should not happen.
-      CGAL_kernel_assertion(false);
-      return visitor.result(false);
+    default:
+      CGAL_unreachable();
     }
 
   case COLLINEAR:
@@ -190,14 +189,12 @@ do_intersect_coplanar(const typename K::Triangle_3& t,
       return visitor.result(coplanar_orientation(*a,*c,p) != POSITIVE);
       // case pqc == COLLINEAR is imposiible
 
-    default: // should not happen.
-      CGAL_kernel_assertion(false);
-      return visitor.result(false);
+    default:
+      CGAL_unreachable();
     }
 
-  default: // should not happen.
-    CGAL_kernel_assertion(false);
-    return visitor.result(false);
+  default:
+    CGAL_unreachable();
   }
 }
 
@@ -262,9 +259,8 @@ do_intersect(const typename K::Triangle_3& t,
       return visitor.result(true);
     }
     // case COPLANAR: should not happen
-    default: // should not happen.
-      CGAL_kernel_assertion(false);
-      return visitor.result(false);
+    default:
+      CGAL_unreachable();
     }
 
   case NEGATIVE:
@@ -292,9 +288,8 @@ do_intersect(const typename K::Triangle_3& t,
 
       // case COPLANAR: should not happen
 
-    default: // should not happen.
-      CGAL_kernel_assertion(false);
-      return visitor.result(false);
+    default:
+      CGAL_unreachable();
     }
 
   case COPLANAR: // p belongs to the triangle's supporting plane
@@ -316,14 +311,12 @@ do_intersect(const typename K::Triangle_3& t,
 
       // case COPLANAR: should not happen
 
-    default: // should not happen.
-      CGAL_kernel_assertion(false);
-      return visitor.result(false);
+    default:
+      CGAL_unreachable();
     }
 
-  default: // should not happen.
-    CGAL_kernel_assertion(false);
-    return visitor.result(false);
+  default:
+    CGAL_unreachable();
   }
 }
 
diff --git a/Intersections_3/include/CGAL/Intersections_3/internal/Segment_3_Triangle_3_do_intersect.h b/Intersections_3/include/CGAL/Intersections_3/internal/Segment_3_Triangle_3_do_intersect.h
index 23fc5d897f43..fcc929708eab 100644
--- a/Intersections_3/include/CGAL/Intersections_3/internal/Segment_3_Triangle_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/Intersections_3/internal/Segment_3_Triangle_3_do_intersect.h
@@ -15,7 +15,7 @@
 
 #include <CGAL/enum.h>
 #include <CGAL/kernel_assertions.h>
-
+#include <CGAL/assertions.h>
 namespace CGAL {
 namespace Intersections {
 namespace internal {
@@ -79,9 +79,8 @@ bool do_intersect_coplanar(const typename K::Point_3& A,
       // a is isolated on the positive side
       return coplanar_orientation(*a,*b,q) != NEGATIVE
           && coplanar_orientation(*c,*a,p) != NEGATIVE;
-    default:// should not happen.
-      CGAL_kernel_assertion(false);
-      return false;
+    default:
+      CGAL_unreachable();
     }
   case NEGATIVE:
     switch ( pqb ) {
@@ -109,9 +108,8 @@ bool do_intersect_coplanar(const typename K::Point_3& A,
       return coplanar_orientation(*a,*b,p) != NEGATIVE
           && coplanar_orientation(*c,*a,q) != NEGATIVE;
 
-    default:// should not happen.
-      CGAL_kernel_assertion(false);
-      return false;
+    default:
+      CGAL_unreachable();
     }
   case COLLINEAR:
     switch ( pqb ) {
@@ -139,14 +137,11 @@ bool do_intersect_coplanar(const typename K::Point_3& A,
       // case pqc == COLLINEAR is impossible since the triangle is
       // assumed to be non flat
 
-    default:// should not happen.
-      CGAL_kernel_assertion(false);
-      return false;
-
+    default:
+      CGAL_unreachable();
     }
-  default:// should not happen.
-    CGAL_kernel_assertion(false);
-    return false;
+  default:
+    CGAL_unreachable();
   }
 }
 
@@ -215,9 +210,8 @@ do_intersect(const typename K::Triangle_3& t,
       return orientation(p,q,a,b) != POSITIVE
           && orientation(p,q,b,c) != POSITIVE
           && orientation(p,q,c,a) != POSITIVE;
-    default: // should not happen.
-      CGAL_kernel_assertion(false);
-      return false;
+    default:
+      CGAL_unreachable();
     }
   case NEGATIVE:
     switch ( abcq ) {
@@ -237,9 +231,8 @@ do_intersect(const typename K::Triangle_3& t,
           && orientation(q,p,b,c) != POSITIVE
           && orientation(q,p,c,a) != POSITIVE;
 
-    default: // should not happen.
-      CGAL_kernel_assertion(false);
-      return false;
+    default:
+      CGAL_unreachable();
     }
   case COPLANAR: // p belongs to the triangle's supporting plane
     switch ( abcq ) {
@@ -259,13 +252,11 @@ do_intersect(const typename K::Triangle_3& t,
       // supporting plane
       return do_intersect_coplanar(t,s,k);
 
-    default: // should not happen.
-      CGAL_kernel_assertion(false);
-      return false;
+    default:
+      CGAL_unreachable();
     }
-  default: // should not happen.
-    CGAL_kernel_assertion(false);
-    return false;
+  default:
+    CGAL_unreachable();
   }
 }
 
diff --git a/Intersections_3/include/CGAL/Intersections_3/internal/Triangle_3_Triangle_3_do_intersect.h b/Intersections_3/include/CGAL/Intersections_3/internal/Triangle_3_Triangle_3_do_intersect.h
index 0ab18e3e0c8c..cd2fcfe1f62d 100644
--- a/Intersections_3/include/CGAL/Intersections_3/internal/Triangle_3_Triangle_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/Intersections_3/internal/Triangle_3_Triangle_3_do_intersect.h
@@ -15,6 +15,7 @@
 
 #include <CGAL/enum.h>
 #include <CGAL/kernel_assertions.h>
+#include <CGAL/assertions.h>
 #include <CGAL/Uncertain.h>
 
 namespace CGAL {
@@ -304,21 +305,18 @@ do_intersect(const typename K::Triangle_3& t1,
 
             case COPLANAR:
               return do_intersect_coplanar(t1,t2,k);
-            default: // should not happen.
-              CGAL_kernel_assertion(false);
-              return false;
+            default:
+              CGAL_unreachable();
           }
           break;
 
-        default: // should not happen.
-          CGAL_kernel_assertion(false);
-          return false;
+        default:
+          CGAL_unreachable();
       }
       break;
 
-    default: // should not happen.
-      CGAL_kernel_assertion(false);
-      return false;
+    default:
+      CGAL_unreachable();
   }
 
   const Point_3* s_min2;
@@ -429,21 +427,18 @@ do_intersect(const typename K::Triangle_3& t1,
               // since the triangles are assumed to be non-flat
 
               return do_intersect_coplanar(t1,t2,k);
-            default: // should not happen.
-              CGAL_kernel_assertion(false);
-              return false;
+            default:
+              CGAL_unreachable();
           }
           break;
 
-        default: // should not happen.
-          CGAL_kernel_assertion(false);
-          return false;
+        default:
+          CGAL_unreachable();
       }
       break;
 
-    default: // should not happen.
-      CGAL_kernel_assertion(false);
-      return false;
+    default:
+      CGAL_unreachable();
   }
 
   return (orientation(*s_min1,*t_min1,*s_min2,*t_min2) != POSITIVE) &&
diff --git a/Kinetic_space_partition/include/CGAL/KSP_3/Finalizer.h b/Kinetic_space_partition/include/CGAL/KSP_3/Finalizer.h
index 8b1c033e8b44..08cf676664ea 100644
--- a/Kinetic_space_partition/include/CGAL/KSP_3/Finalizer.h
+++ b/Kinetic_space_partition/include/CGAL/KSP_3/Finalizer.h
@@ -414,8 +414,7 @@ class Finalizer {
       return true;
     }
 
-    CGAL_assertion(false);
-    return false;
+    CGAL_unreachable();
   }
 
   IVertex non_collinear_vertex(const PFace& pface, const IEdge& iedge) const {
diff --git a/Kinetic_space_partition/include/CGAL/KSP_3/Intersection_graph.h b/Kinetic_space_partition/include/CGAL/KSP_3/Intersection_graph.h
index e86d696bc0b8..99b19ceb13d2 100644
--- a/Kinetic_space_partition/include/CGAL/KSP_3/Intersection_graph.h
+++ b/Kinetic_space_partition/include/CGAL/KSP_3/Intersection_graph.h
@@ -419,10 +419,6 @@ class Intersection_graph {
     return m_graph[edge].crossed.count(sp_idx) == 1;
   }
 
-  void set_crossed(const Edge_descriptor& edge, std::size_t sp_idx) {
-    CGAL_assertion(false);
-    m_graph[edge].crossed.insert(sp_idx);
-  }
 };
 
 template<typename GeomTraits, typename IntersectionKernel> std::size_t Intersection_graph<GeomTraits, IntersectionKernel>::Edge_property::edge_counter = 0;
diff --git a/Lab/demo/Lab/Plugins/PCA/Affine_transform_plugin.cpp b/Lab/demo/Lab/Plugins/PCA/Affine_transform_plugin.cpp
index 0edc6f05f184..0231529e6928 100644
--- a/Lab/demo/Lab/Plugins/PCA/Affine_transform_plugin.cpp
+++ b/Lab/demo/Lab/Plugins/PCA/Affine_transform_plugin.cpp
@@ -728,7 +728,7 @@ end()
       endPolygonMesh(transform_matrix);
     break;
     default:
-      CGAL_assertion(false);
+      CGAL_unreachable();
   }
 
   dockWidget->hide();
diff --git a/Lab/demo/Lab/Plugins/PMP/Smoothing_plugin.cpp b/Lab/demo/Lab/Plugins/PMP/Smoothing_plugin.cpp
index 91673050de35..f2f4ec90570c 100644
--- a/Lab/demo/Lab/Plugins/PMP/Smoothing_plugin.cpp
+++ b/Lab/demo/Lab/Plugins/PMP/Smoothing_plugin.cpp
@@ -379,11 +379,6 @@ public Q_SLOTS:
       selection_item->poly_item_changed();
       selection_item->changed_with_poly_item();
     }
-    else
-    {
-      std::cerr << "Something's gone wrong.\n";
-      CGAL_assertion(false);
-    }
 
     QApplication::restoreOverrideCursor();
   }
diff --git a/Linear_cell_complex/include/CGAL/CMap_linear_cell_complex_storages_with_index.h b/Linear_cell_complex/include/CGAL/CMap_linear_cell_complex_storages_with_index.h
index c85b1476fb9a..3fb7e1c2ab08 100644
--- a/Linear_cell_complex/include/CGAL/CMap_linear_cell_complex_storages_with_index.h
+++ b/Linear_cell_complex/include/CGAL/CMap_linear_cell_complex_storages_with_index.h
@@ -189,14 +189,10 @@ namespace CGAL {
     void init_storage()
     {
       // Allocate a dart for null_dart_descriptor
-      assert(mdarts.empty()); // the compact container is empty
-      Dart_index local_null_dart_descriptor = mdarts.emplace();
-      if(local_null_dart_descriptor!=0)
-      {
-        std::cerr<<"[ERROR] fatal in CMap_linear_cell_complex_storage_with_index::init_storage"
-                 <<std::endl;
-        CGAL_assertion(false);
-      }
+      CGAL_assertion(mdarts.empty()); // the compact container is empty
+      CGAL_assertion_code( Dart_index local_null_dart_descriptor = ) mdarts.emplace();
+      CGAL_assertion_msg(local_null_dart_descriptor==0,
+                          "[ERROR] fatal in CMap_linear_cell_complex_storage_with_index::init_storage");
     }
 
     void clear_storage()
diff --git a/Mesh_3/include/CGAL/Mesh_3/C3T3_helpers.h b/Mesh_3/include/CGAL/Mesh_3/C3T3_helpers.h
index b0de017c924f..0f9d64487af5 100644
--- a/Mesh_3/include/CGAL/Mesh_3/C3T3_helpers.h
+++ b/Mesh_3/include/CGAL/Mesh_3/C3T3_helpers.h
@@ -73,10 +73,8 @@ class Intrusive_list {
   }
 
 
-  Intrusive_list(const Intrusive_list& )
-  {
-    CGAL_assertion(false);
-  }
+  Intrusive_list(const Intrusive_list& ) = delete;
+
 
 #ifdef CGAL_CONSTRUCT_INTRUSIVE_LIST_RANGE_CONSTRUCTOR
   template <typename IT>
diff --git a/Mesh_3/include/CGAL/Mesh_3/Lloyd_move.h b/Mesh_3/include/CGAL/Mesh_3/Lloyd_move.h
index 74dbb09b2ca5..9bb07ec9d5dd 100644
--- a/Mesh_3/include/CGAL/Mesh_3/Lloyd_move.h
+++ b/Mesh_3/include/CGAL/Mesh_3/Lloyd_move.h
@@ -100,9 +100,7 @@ class Lloyd_move
         break;
       default:
         // Should not happen
-        CGAL_assertion(false);
-        return CGAL::NULL_VECTOR;
-        break;
+        CGAL_unreachable();
     }
 
     return CGAL::NULL_VECTOR;
diff --git a/Mesh_3/include/CGAL/Mesh_3/Robust_intersection_traits_3.h b/Mesh_3/include/CGAL/Mesh_3/Robust_intersection_traits_3.h
index 4bb670cbaa98..19ac20f0702b 100644
--- a/Mesh_3/include/CGAL/Mesh_3/Robust_intersection_traits_3.h
+++ b/Mesh_3/include/CGAL/Mesh_3/Robust_intersection_traits_3.h
@@ -387,9 +387,8 @@ ts_intersection(const typename K::Triangle_3 &t,
         // Mesh_3, because if the intersection is not a point, it is
         // ignored anyway.
         return result_type();
-      default: // should not happen.
-        CGAL_kernel_assertion(false);
-        return result_type();
+      default:
+        CGAL_unreachable();
       }
   }
 }
diff --git a/Mesh_3/include/CGAL/Mesh_domain_with_polyline_features_3.h b/Mesh_3/include/CGAL/Mesh_domain_with_polyline_features_3.h
index ddb1ba1109f6..11189652b0f0 100644
--- a/Mesh_3/include/CGAL/Mesh_domain_with_polyline_features_3.h
+++ b/Mesh_3/include/CGAL/Mesh_domain_with_polyline_features_3.h
@@ -976,12 +976,7 @@ Mesh_domain_with_polyline_features_3<MD_>::
 point_corner_index(const Point_3& p) const
 {
   typename Corners::const_iterator p_index_it = corners_.find(p);
-  if ( p_index_it == corners_.end() )
-  {
-    CGAL_assertion(false);
-    return Index();
-  }
-
+  CGAL_assertion( p_index_it != corners_.end());
   return p_index_it->second;
 }
 
diff --git a/Optimal_bounding_box/include/CGAL/Optimal_bounding_box/internal/optimize_2.h b/Optimal_bounding_box/include/CGAL/Optimal_bounding_box/internal/optimize_2.h
index ae450d781e8d..e24b50b51627 100644
--- a/Optimal_bounding_box/include/CGAL/Optimal_bounding_box/internal/optimize_2.h
+++ b/Optimal_bounding_box/include/CGAL/Optimal_bounding_box/internal/optimize_2.h
@@ -169,6 +169,7 @@ void optimize_along_OBB_axes(typename Traits::Matrix& rot,
 
   auto it = std::min_element(volumes.begin(), volumes.end());
   typename std::iterator_traits<decltype(it)>::difference_type d = std::distance(volumes.begin(), it);
+  CGAL_assertion(d == 0 || d == 1 || d == 2);
 
 #ifdef CGAL_OPTIMAL_BOUNDING_BOX_DEBUG_PP
   std::cout << "volumes: " << volumes[0] << " " << volumes[1] << " " << volumes[2] << std::endl;
@@ -212,10 +213,6 @@ void optimize_along_OBB_axes(typename Traits::Matrix& rot,
 
     rot = opt * rot;
   }
-  else
-  {
-    CGAL_assertion(false);
-  }
 }
 
 // This operation makes no sense if an exact number type is used, so skip it, if so
diff --git a/Poisson_surface_reconstruction_3/include/CGAL/Poisson_reconstruction_function.h b/Poisson_surface_reconstruction_3/include/CGAL/Poisson_reconstruction_function.h
index ae2544567d73..23bb0f269339 100644
--- a/Poisson_surface_reconstruction_3/include/CGAL/Poisson_reconstruction_function.h
+++ b/Poisson_surface_reconstruction_3/include/CGAL/Poisson_reconstruction_function.h
@@ -1128,11 +1128,7 @@ class Poisson_reconstruction_function
     }
     while(circ != done);
 
-    if(voronoi_points.size() < 3)
-    {
-      CGAL_assertion(false);
-      return 0.0;
-    }
+    CGAL_assertion(! (voronoi_points.size() < 3));
 
     // sum up areas
     FT area = 0.0;
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Corefinement/intersect_triangle_and_segment_3.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Corefinement/intersect_triangle_and_segment_3.h
index 652d0b09952c..c34dc8aadaed 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Corefinement/intersect_triangle_and_segment_3.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Corefinement/intersect_triangle_and_segment_3.h
@@ -126,9 +126,8 @@ intersection_type(
       // p sees the triangle in counterclockwise order
     return find_intersection(p,q,a,b,c,h_2,tm2,false,true);
 
-    default: // should not happen.
-      CGAL_assertion(false);
-      return result_type(EMPTY,GT::null_halfedge(),false,false);
+    default:
+      CGAL_unreachable();
     }
   case NEGATIVE:
     switch ( abcq ) {
@@ -143,9 +142,8 @@ intersection_type(
       // q belongs to the triangle's supporting plane
       // p sees the triangle in clockwise order
       return find_intersection(q,p,a,b,c,h_2,tm2,false,true);
-    default: // should not happen.
-      CGAL_assertion(false);
-      return result_type(EMPTY,GT::null_halfedge(),false,false);
+    default:
+      CGAL_unreachable();
     }
   case COPLANAR: // p belongs to the triangle's supporting plane
     switch ( abcq ) {
@@ -163,13 +161,11 @@ intersection_type(
         return result_type(COPLANAR_TRIANGLES,GT::null_halfedge(),true,true);
       return result_type(EMPTY,GT::null_halfedge(),true,true);
 
-    default: // should not happen.
-      CGAL_assertion(false);
-      return result_type(EMPTY,GT::null_halfedge(),false,false);
+    default:
+      CGAL_unreachable();
     }
-  default: // should not happen.
-    CGAL_assertion(false);
-    return result_type(EMPTY,GT::null_halfedge(),false,false);
+  default:
+    CGAL_unreachable();
   }
 }
 
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Isotropic_remeshing/remesh_impl.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Isotropic_remeshing/remesh_impl.h
index 4d5622c6f0d8..b2188894a679 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Isotropic_remeshing/remesh_impl.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Isotropic_remeshing/remesh_impl.h
@@ -1940,7 +1940,7 @@ namespace internal {
         else if(is_on_mesh(h))          nb_mesh++;
         else if(is_on_border(h))        nb_border++;
         else if(is_an_isolated_constraint(h)) nb_isolated++;
-        else CGAL_assertion(false);
+        else CGAL_unreachable();
       }
       CGAL_USE(nb_border);
       CGAL_USE(nb_mesh);
diff --git a/Segment_Delaunay_graph_Linf_2/include/CGAL/Segment_Delaunay_graph_Linf_2/Basic_predicates_C2.h b/Segment_Delaunay_graph_Linf_2/include/CGAL/Segment_Delaunay_graph_Linf_2/Basic_predicates_C2.h
index 7f1267098670..961bba0cf7ac 100644
--- a/Segment_Delaunay_graph_Linf_2/include/CGAL/Segment_Delaunay_graph_Linf_2/Basic_predicates_C2.h
+++ b/Segment_Delaunay_graph_Linf_2/include/CGAL/Segment_Delaunay_graph_Linf_2/Basic_predicates_C2.h
@@ -641,9 +641,7 @@ struct Basic_predicates_C2
         CGAL_SDG_DEBUG(std::cout << "ON_BOUNDED_SIDE" << std::endl;);
         return ON_BOUNDED_SIDE;
       default:
-        CGAL_SDG_DEBUG(std::cout << "error: should never reach here";);
-        CGAL_assertion( false );
-        return ON_BOUNDARY;
+        CGAL_unreachable();
     }
   }
 
diff --git a/Segment_Delaunay_graph_Linf_2/include/CGAL/Segment_Delaunay_graph_Linf_2/Vertex_conflict_C2.h b/Segment_Delaunay_graph_Linf_2/include/CGAL/Segment_Delaunay_graph_Linf_2/Vertex_conflict_C2.h
index c78bc09543c2..6307e1bf2f5e 100644
--- a/Segment_Delaunay_graph_Linf_2/include/CGAL/Segment_Delaunay_graph_Linf_2/Vertex_conflict_C2.h
+++ b/Segment_Delaunay_graph_Linf_2/include/CGAL/Segment_Delaunay_graph_Linf_2/Vertex_conflict_C2.h
@@ -780,7 +780,7 @@ class Vertex_conflict_C2
 
         // philaris: execution should never reach here
         // philaris: code added to avoid warnings on some compilers
-        CGAL_assertion( false );
+        CGAL_assertion(false);
         return ZERO;
 
       } // end of case where segment is neither horizontal nor vertical
@@ -877,7 +877,7 @@ class Vertex_conflict_C2
             otherpnt = seg.source();
           } else {
             // unreachable
-            CGAL_assertion( false );
+            CGAL_assertion(false);
           }
 
           lhor = compute_horizontal_side_line(
@@ -1138,7 +1138,7 @@ class Vertex_conflict_C2
             otherpnt = seg.source();
           } else {
             // unreachable
-            CGAL_assertion( false );
+            CGAL_assertion(false);
           }
 
           lhor = compute_horizontal_side_line(
diff --git a/Segment_Delaunay_graph_Linf_2/include/CGAL/Segment_Delaunay_graph_Linf_2/Voronoi_vertex_ring_C2.h b/Segment_Delaunay_graph_Linf_2/include/CGAL/Segment_Delaunay_graph_Linf_2/Voronoi_vertex_ring_C2.h
index cf35f9476c87..4675a46348ac 100644
--- a/Segment_Delaunay_graph_Linf_2/include/CGAL/Segment_Delaunay_graph_Linf_2/Voronoi_vertex_ring_C2.h
+++ b/Segment_Delaunay_graph_Linf_2/include/CGAL/Segment_Delaunay_graph_Linf_2/Voronoi_vertex_ring_C2.h
@@ -592,8 +592,8 @@ class Voronoi_vertex_ring_C2
     const unsigned int bq = bearing(lq);
     const unsigned int br = bearing(lr);
     const unsigned int bdiff = bearing_diff(bq, br);
-    CGAL_assertion( bdiff != 0 );
-    CGAL_assertion( bdiff != 7 );
+    CGAL_assertion( bdiff > 0 );
+    CGAL_assertion( bdiff < 7 );
 
     if (bdiff == 1) {
       compute_pss_corner_and_pt(p, q, r, lq, lr, bq, br);
@@ -605,8 +605,6 @@ class Voronoi_vertex_ring_C2
       compute_pss_side_p_known(p, q, r, lq, lr, bq, br);
     } else if (bdiff == 6) {
       compute_pss_lines_side(p, lq, lr, (br+1)%8);
-    } else {
-      CGAL_assertion( false );
     }
     CGAL_assertion_code( is_v_computed = true );
     CGAL_assertion( oriented_side_of_line(lq, this->point()) != ZERO );
diff --git a/Segment_Delaunay_graph_Linf_2/include/CGAL/Segment_Delaunay_graph_Linf_2/Voronoi_vertex_sqrt_field_new_C2.h b/Segment_Delaunay_graph_Linf_2/include/CGAL/Segment_Delaunay_graph_Linf_2/Voronoi_vertex_sqrt_field_new_C2.h
index 8ea071730250..bad4f8fc5ab3 100644
--- a/Segment_Delaunay_graph_Linf_2/include/CGAL/Segment_Delaunay_graph_Linf_2/Voronoi_vertex_sqrt_field_new_C2.h
+++ b/Segment_Delaunay_graph_Linf_2/include/CGAL/Segment_Delaunay_graph_Linf_2/Voronoi_vertex_sqrt_field_new_C2.h
@@ -1106,8 +1106,7 @@ class Voronoi_vertex_sqrt_field_new_C2
     const Bearing bq = bearing(lq);
     const Bearing br = bearing(lr);
     const Bearing bdiff = bearing_diff(bq, br);
-    CGAL_assertion( bdiff != 0 );
-    CGAL_assertion( bdiff != 7 );
+    CGAL_assertion( bdiff  > 0 &&  bdiff < 7 );
 
     if (bdiff == 1) {
       compute_pss_corner_and_pt(p, lq, lr, bq, br);
@@ -1119,9 +1118,8 @@ class Voronoi_vertex_sqrt_field_new_C2
       compute_pss_side_p_known(p, q, r, lq, lr, bq, br);
     } else if (bdiff == 6) {
       compute_pss_lines_side(p, lq, lr, (br+1)%8);
-    } else {
-      CGAL_assertion( false );
     }
+
     CGAL_assertion( oriented_side_of_line(lq, this->point()) != ZERO );
     CGAL_assertion( oriented_side_of_line(lr, this->point()) != ZERO );
   }
diff --git a/Straight_skeleton_2/include/CGAL/Trisegment_2.h b/Straight_skeleton_2/include/CGAL/Trisegment_2.h
index ce7fa34a79c0..38ec084673b5 100644
--- a/Straight_skeleton_2/include/CGAL/Trisegment_2.h
+++ b/Straight_skeleton_2/include/CGAL/Trisegment_2.h
@@ -148,7 +148,7 @@ class Trisegment_2
       case TRISEGMENT_COLLINEARITY_02:
         return e(2);
       default:
-        CGAL_assertion(false);
+        CGAL_unreachable();
         return e(0); // arbitrary, meaningless value because a const& is expected
     }
   }
@@ -166,8 +166,7 @@ class Trisegment_2
       case TRISEGMENT_COLLINEARITY_02:
         return w(2);
       default:
-        CGAL_assertion(false);
-        return w(0); // arbitrary, meaningless value because a const& is expected
+        CGAL_unreachable();
     }
   }
 
diff --git a/Surface_mesh_deformation/include/CGAL/Surface_mesh_deformation.h b/Surface_mesh_deformation/include/CGAL/Surface_mesh_deformation.h
index a536e13ddaed..f1129a6e79f0 100644
--- a/Surface_mesh_deformation/include/CGAL/Surface_mesh_deformation.h
+++ b/Surface_mesh_deformation/include/CGAL/Surface_mesh_deformation.h
@@ -556,6 +556,7 @@ class Surface_mesh_deformation
     erase_control_vertex(vd); // also erase from being control
 
     typename std::vector<vertex_descriptor>::iterator it = std::find(roi.begin(), roi.end(), vd);
+    CGAL_assertion_msg(it != roi.end(), "inconsistency between is_roi_map, and roi vector");
     if(it != roi.end())
     {
       is_roi_map[id(vd)] = false;
@@ -564,8 +565,6 @@ class Surface_mesh_deformation
       need_preprocess_both();
       return true;
     }
-
-    CGAL_assertion(false); // inconsistency between is_roi_map, and roi vector!
     return false;
   }
 
diff --git a/Surface_mesh_parameterization/include/CGAL/Surface_mesh_parameterization/Two_vertices_parameterizer_3.h b/Surface_mesh_parameterization/include/CGAL/Surface_mesh_parameterization/Two_vertices_parameterizer_3.h
index 17cfb22d3a78..f69fe5416e85 100644
--- a/Surface_mesh_parameterization/include/CGAL/Surface_mesh_parameterization/Two_vertices_parameterizer_3.h
+++ b/Surface_mesh_parameterization/include/CGAL/Surface_mesh_parameterization/Two_vertices_parameterizer_3.h
@@ -205,7 +205,7 @@ class Two_vertices_parameterizer_3
       V1_max = zmax;
       break;
     default:
-      CGAL_assertion(false);
+      CGAL_unreachable();
     }
     switch (second_longest_axis)
     {
@@ -225,7 +225,7 @@ class Two_vertices_parameterizer_3
       V2_max = zmax;
       break;
     default:
-      CGAL_assertion(false);
+      CGAL_unreachable();
     }
 
     // Project onto longest bounding box axes,
diff --git a/Surface_mesh_parameterization/include/CGAL/Surface_mesh_parameterization/internal/orbifold_cone_helper.h b/Surface_mesh_parameterization/include/CGAL/Surface_mesh_parameterization/internal/orbifold_cone_helper.h
index 48610f5e5236..3705683ce0cf 100644
--- a/Surface_mesh_parameterization/include/CGAL/Surface_mesh_parameterization/internal/orbifold_cone_helper.h
+++ b/Surface_mesh_parameterization/include/CGAL/Surface_mesh_parameterization/internal/orbifold_cone_helper.h
@@ -122,8 +122,7 @@ void find_start_cone(const ConeMap& cmap,
     return;
   }
 
-  std::cerr << "Error: did not find first cone" << std::endl;
-  CGAL_postcondition(false);
+  CGAL_postcondition_msg(false,"Error: did not find first cone");
 }
 
 // Locate the cone tagged 'First_unique_cone' in the seam mesh.
@@ -143,8 +142,7 @@ void find_start_cone(const ConeMap& cmap,
     return;
   }
 
-  std::cerr << "Error: did not find first cone" << std::endl;
-  CGAL_postcondition(false);
+  CGAL_postcondition_msg(false,"Error: did not find first cone");
 }
 
 /// Check the validity of the input cones in the `Seam_mesh` mesh.
diff --git a/Surface_mesh_topology/include/CGAL/Surface_mesh_topology/internal/Functors_for_face_graph_wrapper.h b/Surface_mesh_topology/include/CGAL/Surface_mesh_topology/internal/Functors_for_face_graph_wrapper.h
index 200ffb829379..52e386b0000f 100644
--- a/Surface_mesh_topology/include/CGAL/Surface_mesh_topology/internal/Functors_for_face_graph_wrapper.h
+++ b/Surface_mesh_topology/include/CGAL/Surface_mesh_topology/internal/Functors_for_face_graph_wrapper.h
@@ -35,17 +35,8 @@ namespace internal {
 ////////////////////////////////////////////////////////////////////////////////
 /// Get_beta
 template<typename HEG, unsigned int i>
-struct Get_beta
-{
-  typedef typename boost::graph_traits<HEG>::halfedge_descriptor Dart_const_descriptor;
+struct Get_beta;
 
-  static Dart_const_descriptor value(const HEG& /*heg*/, Dart_const_descriptor /*dh*/)
-  {
-    std::cout<<"ERROR Get_beta<HEG, "<<i<<">"<<std::endl;
-    CGAL_assertion(false);
-    return nullptr;
-  }
-};
 template<typename HEG>
 struct Get_beta<HEG, 0>
 {
diff --git a/TDS_2/include/CGAL/Triangulation_data_structure_2.h b/TDS_2/include/CGAL/Triangulation_data_structure_2.h
index 7eb651ef4074..4aa6fdafec0a 100644
--- a/TDS_2/include/CGAL/Triangulation_data_structure_2.h
+++ b/TDS_2/include/CGAL/Triangulation_data_structure_2.h
@@ -1118,8 +1118,8 @@ insert_dim_up(Vertex_handle w,  bool orient)
     }
     break;
   default:
-    CGAL_assertion(false);
-    break;  }
+    CGAL_unreachable();
+  }
   return v;
 }
 
diff --git a/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/smooth_vertices.h b/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/smooth_vertices.h
index fd9981c1426a..aca5c18f196a 100644
--- a/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/smooth_vertices.h
+++ b/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/smooth_vertices.h
@@ -871,13 +871,9 @@ std::size_t smooth_vertices_on_surfaces(C3t3& c3t3,
           {
             const auto intersection = proj.value().first;
             using Segment = typename Tr::Geom_traits::Segment_3;
-            if (const Segment* s = std::get_if<Segment>(&intersection))
-              return CGAL::midpoint(s->source(), s->target());
-            else
-            {
-              CGAL_assertion(false);
-              return std::nullopt;
-            }
+            const Segment* s = std::get_if<Segment>(&intersection);
+            CGAL_assertion(s != nullptr);
+            return CGAL::midpoint(s->source(), s->target());
           };
 
         const auto n = vertices_normals.at(v).at(si);
diff --git a/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/tetrahedral_remeshing_helpers.h b/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/tetrahedral_remeshing_helpers.h
index 2e93f2f8335a..c39c85f31111 100644
--- a/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/tetrahedral_remeshing_helpers.h
+++ b/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/tetrahedral_remeshing_helpers.h
@@ -844,7 +844,7 @@ void set_index(typename C3t3::Vertex_handle v, const C3t3& c3t3)
   case -1://far points from concurrent Mesh_3
     break;
   default:
-    CGAL_assertion(false);
+    CGAL_unreachable();
   }
 }
 
diff --git a/Triangulation_2/include/CGAL/Constrained_Delaunay_triangulation_2.h b/Triangulation_2/include/CGAL/Constrained_Delaunay_triangulation_2.h
index 714e9295b61f..6e8d9ba164cc 100644
--- a/Triangulation_2/include/CGAL/Constrained_Delaunay_triangulation_2.h
+++ b/Triangulation_2/include/CGAL/Constrained_Delaunay_triangulation_2.h
@@ -489,8 +489,7 @@ class Constrained_Delaunay_triangulation_2
       pit = propagate_conflicts(p,fh,2,pit);
       return pit;
     }
-    CGAL_assertion(false);
-    return std::make_pair(fit,eit);
+    CGAL_unreachable();
   }
 
   template <class OutputItFaces>
diff --git a/Triangulation_2/include/CGAL/Delaunay_triangulation_2.h b/Triangulation_2/include/CGAL/Delaunay_triangulation_2.h
index 617e8c23a8a4..2b616a8ca5cd 100644
--- a/Triangulation_2/include/CGAL/Delaunay_triangulation_2.h
+++ b/Triangulation_2/include/CGAL/Delaunay_triangulation_2.h
@@ -418,8 +418,7 @@ class Delaunay_triangulation_2
         pit = propagate_conflicts(p,fh,2,pit);
         return pit;
     }
-    CGAL_assertion(false);
-    return std::make_pair(fit,eit);
+    CGAL_unreachable();
   }
 
   template <class OutputItFaces>
diff --git a/Triangulation_2/include/CGAL/Regular_triangulation_2.h b/Triangulation_2/include/CGAL/Regular_triangulation_2.h
index 54938928e5c4..b1971f8bbf50 100644
--- a/Triangulation_2/include/CGAL/Regular_triangulation_2.h
+++ b/Triangulation_2/include/CGAL/Regular_triangulation_2.h
@@ -640,8 +640,7 @@ class Regular_triangulation_2
         }
         return  make_triple(fit, eit, vit);
     }
-    CGAL_assertion(false);
-    return make_triple(fit, eit, vit);
+    CGAL_unreachable();
   }
 
   template <class OutputItFaces, class OutputItBoundaryEdges>
diff --git a/Triangulation_2/include/CGAL/Triangulation_2.h b/Triangulation_2/include/CGAL/Triangulation_2.h
index 433ea5cb5af3..dc0de4ed4745 100644
--- a/Triangulation_2/include/CGAL/Triangulation_2.h
+++ b/Triangulation_2/include/CGAL/Triangulation_2.h
@@ -1488,8 +1488,7 @@ insert(const Point& p, Locate_type lt, Face_handle loc, int li)
   case VERTEX:
     return loc->vertex(li);
   }
-  CGAL_assertion(false); // locate step failed
-  return Vertex_handle();
+  CGAL_unreachable();
 }
 
 
diff --git a/Triangulation_2/include/CGAL/Triangulation_hierarchy_2.h b/Triangulation_2/include/CGAL/Triangulation_hierarchy_2.h
index 295132483846..fd788a3e61a1 100644
--- a/Triangulation_2/include/CGAL/Triangulation_hierarchy_2.h
+++ b/Triangulation_2/include/CGAL/Triangulation_hierarchy_2.h
@@ -251,8 +251,7 @@ class Triangulation_hierarchy_2
   Vertex_handle
   nearest_vertex_dispatch(const Point&, Face_handle, Tag_true) const
   {
-    CGAL_assertion(false);
-    return Vertex_handle();
+    CGAL_unreachable();
   }
 
   void  locate_in_all(const Point& p,
diff --git a/Triangulation_3/include/CGAL/Triangulation_segment_traverser_3.h b/Triangulation_3/include/CGAL/Triangulation_segment_traverser_3.h
index 6f25e793fda1..6b2288f5d338 100644
--- a/Triangulation_3/include/CGAL/Triangulation_segment_traverser_3.h
+++ b/Triangulation_3/include/CGAL/Triangulation_segment_traverser_3.h
@@ -944,9 +944,7 @@ class Triangulation_segment_simplex_iterator_3
     default:
       CGAL_unreachable();
     }
-    //should not be reached
     CGAL_unreachable();
-    return false;
   }
 
   bool cell_has_edge(const Cell_handle ch, const Edge& e) const
@@ -1056,7 +1054,7 @@ class Triangulation_segment_simplex_iterator_3
     } while (++circ != end);
 
     std::cerr << "There is no facet shared by e and v" << std::endl;
-    CGAL_unreachable();
+    CGAL_assertion(false);
     return Facet(Cell_handle(), 0);
   }
 
@@ -1073,7 +1071,7 @@ class Triangulation_segment_simplex_iterator_3
     } while (++circ != end);
 
     std::cerr << "There is no cell shared by e and v" << std::endl;
-    CGAL_unreachable();
+    CGAL_assertion(false);
     return Cell_handle();
   }
 
diff --git a/Triangulation_on_sphere_2/include/CGAL/Triangulation_on_sphere_2.h b/Triangulation_on_sphere_2/include/CGAL/Triangulation_on_sphere_2.h
index 545e54ac112e..6b26605356ca 100644
--- a/Triangulation_on_sphere_2/include/CGAL/Triangulation_on_sphere_2.h
+++ b/Triangulation_on_sphere_2/include/CGAL/Triangulation_on_sphere_2.h
@@ -780,7 +780,7 @@ march_locate_2D(Face_handle f,
           }
         }
 
-        CGAL_precondition(false);
+        CGAL_assertion(false);
       }
     }
 
@@ -972,9 +972,7 @@ march_locate_2D(Face_handle f,
       }
       default:
       {
-        // impossible
-        CGAL_assertion(false);
-        return f;
+        CGAL_unreachable();
       }
     }
 
diff --git a/Visibility_2/include/CGAL/Rotational_sweep_visibility_2.h b/Visibility_2/include/CGAL/Rotational_sweep_visibility_2.h
index fd7bfd719a8e..bbd74ca53d87 100644
--- a/Visibility_2/include/CGAL/Rotational_sweep_visibility_2.h
+++ b/Visibility_2/include/CGAL/Rotational_sweep_visibility_2.h
@@ -238,7 +238,6 @@ class Rotational_sweep_visibility_2 {
       }
 
       CGAL_unreachable();
-      return false;
     }
 
   };