diff --git a/drf_spectacular/openapi.py b/drf_spectacular/openapi.py
index ca1967bb..13998ff2 100644
--- a/drf_spectacular/openapi.py
+++ b/drf_spectacular/openapi.py
@@ -35,10 +35,11 @@
     build_mocked_view, build_object_type, build_parameter_type, build_serializer_context,
     filter_supported_arguments, follow_field_source, follow_model_field_lookup, force_instance,
     get_doc, get_list_serializer, get_manager, get_type_hints, get_view_model, is_basic_serializer,
-    is_basic_type, is_field, is_list_serializer, is_list_serializer_customized,
-    is_patched_serializer, is_serializer, is_trivial_string_variation,
-    modify_media_types_for_versioning, resolve_django_path_parameter, resolve_regex_path_parameter,
-    resolve_type_hint, safe_ref, sanitize_specification_extensions, whitelisted,
+    is_basic_type, is_field, is_higher_order_type_hint, is_list_serializer,
+    is_list_serializer_customized, is_patched_serializer, is_serializer,
+    is_trivial_string_variation, modify_media_types_for_versioning, resolve_django_path_parameter,
+    resolve_regex_path_parameter, resolve_type_hint, safe_ref, sanitize_specification_extensions,
+    whitelisted,
 )
 from drf_spectacular.settings import spectacular_settings
 from drf_spectacular.types import OpenApiTypes
@@ -1338,6 +1339,9 @@ def _get_request_for_media_type(self, serializer, direction='request'):
         elif is_basic_type(serializer):
             schema = build_basic_type(serializer)
             request_body_required = False
+        elif is_higher_order_type_hint(serializer):
+            schema = resolve_type_hint(serializer)
+            request_body_required = False
         elif isinstance(serializer, dict):
             # bypass processing and use given schema directly
             schema = serializer
@@ -1358,6 +1362,7 @@ def _get_response_bodies(self, direction: Direction = 'response') -> _SchemaType
         if (
             is_serializer(response_serializers)
             or is_basic_type(response_serializers)
+            or is_higher_order_type_hint(response_serializers)
             or isinstance(response_serializers, OpenApiResponse)
         ):
             if self.method == 'DELETE':
@@ -1426,6 +1431,8 @@ def _get_response_for_code(self, serializer, status_code, media_types=None, dire
             schema = component.ref
         elif is_basic_type(serializer):
             schema = build_basic_type(serializer)
+        elif is_higher_order_type_hint(serializer):
+            schema = resolve_type_hint(serializer)
         elif isinstance(serializer, dict):
             # bypass processing and use given schema directly
             schema = serializer
diff --git a/drf_spectacular/plumbing.py b/drf_spectacular/plumbing.py
index d35da3aa..ffd54755 100644
--- a/drf_spectacular/plumbing.py
+++ b/drf_spectacular/plumbing.py
@@ -98,6 +98,10 @@ class Choices:  # type: ignore
 T = TypeVar('T')
 
 
+class _Sentinel:
+    pass
+
+
 class UnableToProceedError(Exception):
     pass
 
@@ -1287,6 +1291,15 @@ def _resolve_typeddict(hint):
     )
 
 
+def is_higher_order_type_hint(hint) -> bool:
+    return isinstance(hint, (
+        getattr(types, 'GenericAlias', _Sentinel),
+        getattr(types, 'UnionType', _Sentinel),
+        getattr(typing, '_GenericAlias', _Sentinel),
+        getattr(typing, '_UnionGenericAlias', _Sentinel),
+    ))
+
+
 def resolve_type_hint(hint):
     """ resolve return value type hints to schema """
     origin, args = _get_type_hint_origin(hint)
diff --git a/tests/test_regressions.py b/tests/test_regressions.py
index 9bdac659..c2b2e396 100644
--- a/tests/test_regressions.py
+++ b/tests/test_regressions.py
@@ -1,6 +1,7 @@
 import collections
 import datetime
 import re
+import sys
 import typing
 import uuid
 from decimal import Decimal
@@ -3300,3 +3301,30 @@ class XViewset(viewsets.ReadOnlyModelViewSet):
             'readOnly': True
         },
     }
+
+
+def test_extend_schema_higher_order_types(no_warnings):
+    cases = [
+        (typing.List[int], {'items': {'type': 'integer'}, 'type': 'array'}),
+        (typing.Dict[str, int], {'type': 'object', 'additionalProperties': {'type': 'integer'}}),
+        (typing.Union[int, float], {'oneOf': [{'type': 'integer'}, {'format': 'double', 'type': 'number'}]}),
+        (typing.Set[int], {'items': {'type': 'integer'}, 'type': 'array'}),
+        (typing.Optional[int], {'type': 'integer', 'nullable': True}),
+    ]
+    if sys.version_info >= (3, 10):
+        cases.extend([
+            (list[int], {'items': {'type': 'integer'}, 'type': 'array'}),
+            (dict[str, int], {'type': 'object', 'additionalProperties': {'type': 'integer'}}),
+            (int | float, {'oneOf': [{'type': 'integer'}, {'format': 'double', 'type': 'number'}]}),
+        ])
+
+    for t, ref_schema in cases:
+        @extend_schema(request=t, responses=t)
+        @api_view(['POST'])
+        def view_func(request, format=None):
+            pass  # pragma: no cover
+
+        schema = generate_schema('x', view_function=view_func)
+
+        assert get_response_schema(schema['paths']['/x']['post']) == ref_schema
+        assert get_request_schema(schema['paths']['/x']['post']) == ref_schema