diff --git a/docs/types.rst b/docs/types.rst
index ea4cb14..ca2bfb8 100644
--- a/docs/types.rst
+++ b/docs/types.rst
@@ -186,8 +186,8 @@ Is output as:
    }
 
 
-:class:`typing.Union`
-~~~~~~~~~~~~~~~~~~~~~
+:class:`typing.Union` and :class:`types.UnionType` (``X | Y``)
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
 Avro schema: JSON array of multiple Avro schemas
 
diff --git a/src/py_avro_schema/_schemas.py b/src/py_avro_schema/_schemas.py
index 2759c20..41d5663 100644
--- a/src/py_avro_schema/_schemas.py
+++ b/src/py_avro_schema/_schemas.py
@@ -24,6 +24,7 @@
 import enum
 import inspect
 import sys
+import types
 import uuid
 from typing import (
     TYPE_CHECKING,
@@ -572,6 +573,11 @@ class UnionSchema(Schema):
     def handles_type(cls, py_type: Type) -> bool:
         """Whether this schema class can represent a given Python class"""
         origin = get_origin(py_type)
+
+        # Support for `X | Y` syntax available in Python 3.10+
+        # equivalent to `typing.Union[X, Y]`
+        if getattr(types, "UnionType", None):
+            return origin == Union or origin == types.UnionType  # noqa: E721
         return origin == Union
 
     def __init__(self, py_type: Type[Union[Any]], namespace: Optional[str] = None, options: Option = Option(0)):
diff --git a/tests/test_primitives.py b/tests/test_primitives.py
index 2d2ee6c..191d742 100644
--- a/tests/test_primitives.py
+++ b/tests/test_primitives.py
@@ -11,6 +11,7 @@
 
 import enum
 import re
+import sys
 from typing import (
     Dict,
     List,
@@ -137,6 +138,10 @@ def test_string_tuple():
     expected = {"type": "array", "items": "string"}
     assert_schema(py_type, expected)
 
+    py_type = tuple[str]
+    expected = {"type": "array", "items": "string"}
+    assert_schema(py_type, expected)
+
 
 def test_string_sequence():
     py_type = Sequence[str]
@@ -220,6 +225,16 @@ def test_string_dict_of_dicts():
     }
     assert_schema(py_type, expected)
 
+    py_type = dict[str, dict[str, str]]
+    expected = {
+        "type": "map",
+        "values": {
+            "type": "map",
+            "values": "string",
+        },
+    }
+    assert_schema(py_type, expected)
+
 
 def test_union_string_int():
     py_type = Union[str, int]
@@ -227,12 +242,26 @@ def test_union_string_int():
     assert_schema(py_type, expected)
 
 
+@pytest.mark.skipif(sys.version_info < (3, 10), reason="Requires Python 3.10+")
+def test_union_string_int_py310():
+    py_type = str | int
+    expected = ["string", "long"]
+    assert_schema(py_type, expected)
+
+
 def test_union_string_string_int():
     py_type = Union[str, str, int]
     expected = ["string", "long"]
     assert_schema(py_type, expected)
 
 
+@pytest.mark.skipif(sys.version_info < (3, 10), reason="Requires Python 3.10+")
+def test_union_string_string_int_py310():
+    py_type = str | int | str
+    expected = ["string", "long"]
+    assert_schema(py_type, expected)
+
+
 def test_union_of_union_string_int():
     py_type = Union[str, Union[str, int]]
     expected = ["string", "long"]
@@ -245,6 +274,13 @@ def test_optional_str():
     assert_schema(py_type, expected)
 
 
+@pytest.mark.skipif(sys.version_info < (3, 10), reason="Requires Python 3.10+")
+def test_optional_str_py310():
+    py_type = str | None
+    expected = ["string", "null"]
+    assert_schema(py_type, expected)
+
+
 def test_enum():
     class PyType(enum.Enum):
         RED = "RED"