diff --git a/rest_framework/fields.py b/rest_framework/fields.py
index 1c6425596..613bd325a 100644
--- a/rest_framework/fields.py
+++ b/rest_framework/fields.py
@@ -356,6 +356,10 @@ class Field:
         messages.update(error_messages or {})
         self.error_messages = messages
 
+    # Allow generic typing checking for fields.
+    def __class_getitem__(cls, *args, **kwargs):
+        return cls
+
     def bind(self, field_name, parent):
         """
         Initializes the field name and parent for the field instance.
diff --git a/rest_framework/generics.py b/rest_framework/generics.py
index 55cfafda4..167303321 100644
--- a/rest_framework/generics.py
+++ b/rest_framework/generics.py
@@ -45,6 +45,10 @@ class GenericAPIView(views.APIView):
     # The style to use for queryset pagination.
     pagination_class = api_settings.DEFAULT_PAGINATION_CLASS
 
+    # Allow generic typing checking for generic views.
+    def __class_getitem__(cls, *args, **kwargs):
+        return cls
+
     def get_queryset(self):
         """
         Get the list of items for this view.
diff --git a/rest_framework/request.py b/rest_framework/request.py
index 194be5f6d..93109226d 100644
--- a/rest_framework/request.py
+++ b/rest_framework/request.py
@@ -186,6 +186,10 @@ class Request:
             self.method,
             self.get_full_path())
 
+    # Allow generic typing checking for requests.
+    def __class_getitem__(cls, *args, **kwargs):
+        return cls
+
     def _default_negotiator(self):
         return api_settings.DEFAULT_CONTENT_NEGOTIATION_CLASS()
 
diff --git a/rest_framework/response.py b/rest_framework/response.py
index 495423734..6e756544c 100644
--- a/rest_framework/response.py
+++ b/rest_framework/response.py
@@ -46,6 +46,10 @@ class Response(SimpleTemplateResponse):
             for name, value in headers.items():
                 self[name] = value
 
+    # Allow generic typing checking for responses.
+    def __class_getitem__(cls, *args, **kwargs):
+        return cls
+
     @property
     def rendered_content(self):
         renderer = getattr(self, 'accepted_renderer', None)
diff --git a/tests/test_fields.py b/tests/test_fields.py
index 512f3f789..56e2a45ba 100644
--- a/tests/test_fields.py
+++ b/tests/test_fields.py
@@ -2,6 +2,7 @@ import datetime
 import math
 import os
 import re
+import sys
 import uuid
 from decimal import ROUND_DOWN, ROUND_UP, Decimal
 
@@ -625,6 +626,15 @@ class Test5087Regression:
         assert field.root is parent
 
 
+class TestTyping(TestCase):
+    @pytest.mark.skipif(
+        sys.version_info < (3, 7),
+        reason="subscriptable classes requires Python 3.7 or higher",
+    )
+    def test_field_is_subscriptable(self):
+        assert serializers.Field is serializers.Field["foo"]
+
+
 # Tests for field input and output values.
 # ----------------------------------------
 
diff --git a/tests/test_generics.py b/tests/test_generics.py
index 78dc5afb6..9990389c9 100644
--- a/tests/test_generics.py
+++ b/tests/test_generics.py
@@ -1,3 +1,5 @@
+import sys
+
 import pytest
 from django.db import models
 from django.http import Http404
@@ -698,3 +700,26 @@ class TestSerializer(TestCase):
         serializer = response.serializer
 
         assert serializer.context is context
+
+
+class TestTyping(TestCase):
+    @pytest.mark.skipif(
+        sys.version_info < (3, 7),
+        reason="subscriptable classes requires Python 3.7 or higher",
+    )
+    def test_genericview_is_subscriptable(self):
+        assert generics.GenericAPIView is generics.GenericAPIView["foo"]
+
+    @pytest.mark.skipif(
+        sys.version_info < (3, 7),
+        reason="subscriptable classes requires Python 3.7 or higher",
+    )
+    def test_listview_is_subscriptable(self):
+        assert generics.ListAPIView is generics.ListAPIView["foo"]
+
+    @pytest.mark.skipif(
+        sys.version_info < (3, 7),
+        reason="subscriptable classes requires Python 3.7 or higher",
+    )
+    def test_instanceview_is_subscriptable(self):
+        assert generics.RetrieveAPIView is generics.RetrieveAPIView["foo"]
diff --git a/tests/test_request.py b/tests/test_request.py
index 8c18aea9e..e37aa7dda 100644
--- a/tests/test_request.py
+++ b/tests/test_request.py
@@ -3,6 +3,7 @@ Tests for content parsing, and form-overloaded content parsing.
 """
 import copy
 import os.path
+import sys
 import tempfile
 
 import pytest
@@ -352,3 +353,12 @@ class TestDeepcopy(TestCase):
     def test_deepcopy_works(self):
         request = Request(factory.get('/', secure=False))
         copy.deepcopy(request)
+
+
+class TestTyping(TestCase):
+    @pytest.mark.skipif(
+        sys.version_info < (3, 7),
+        reason="subscriptable classes requires Python 3.7 or higher",
+    )
+    def test_request_is_subscriptable(self):
+        assert Request is Request["foo"]
diff --git a/tests/test_response.py b/tests/test_response.py
index 0d5528dc9..cab19a1eb 100644
--- a/tests/test_response.py
+++ b/tests/test_response.py
@@ -1,3 +1,6 @@
+import sys
+
+import pytest
 from django.test import TestCase, override_settings
 from django.urls import include, path, re_path
 
@@ -283,3 +286,12 @@ class Issue807Tests(TestCase):
         self.assertEqual(resp['Content-Type'], 'text/html; charset=utf-8')
         # self.assertContains(resp, 'Text comes here')
         # self.assertContains(resp, 'Text description.')
+
+
+class TestTyping(TestCase):
+    @pytest.mark.skipif(
+        sys.version_info < (3, 7),
+        reason="subscriptable classes requires Python 3.7 or higher",
+    )
+    def test_response_is_subscriptable(self):
+        assert Response is Response["foo"]