diff --git a/rest_framework/schemas/openapi.py b/rest_framework/schemas/openapi.py
index 0af7510cd..edb2503fd 100644
--- a/rest_framework/schemas/openapi.py
+++ b/rest_framework/schemas/openapi.py
@@ -1,3 +1,4 @@
+import re
 import warnings
 from urllib.parse import urljoin
 
@@ -6,16 +7,22 @@ from django.core.validators import (
     MinLengthValidator, MinValueValidator, RegexValidator, URLValidator
 )
 from django.db import models
-from django.utils.encoding import force_str
+from django.utils.encoding import force_str, smart_text
 
 from rest_framework import exceptions, serializers
 from rest_framework.compat import uritemplate
 from rest_framework.fields import _UnvalidatedField, empty
+from rest_framework.settings import api_settings
+from rest_framework.utils import formatting
 
 from .generators import BaseSchemaGenerator
 from .inspectors import ViewInspector
 from .utils import get_pk_description, is_list_view
 
+# Used in _get_description_section()
+# TODO: ???: move up to base.
+header_regex = re.compile('^[a-zA-Z][0-9A-Za-z_]*:')
+
 # Generator
 
 
@@ -87,10 +94,49 @@ class AutoSchema(ViewInspector):
         'delete': 'Destroy',
     }
 
+    def get_description(self, path, method):
+        """
+        Determine a link description.
+
+        This will be based on the method docstring if one exists,
+        or else the class docstring.
+        """
+        view = self.view
+
+        method_name = getattr(view, 'action', method.lower())
+        method_docstring = getattr(view, method_name, None).__doc__
+        if method_docstring:
+            # An explicit docstring on the method or action.
+            return self._get_description_section(view, method.lower(), formatting.dedent(smart_text(method_docstring)))
+        else:
+            return self._get_description_section(view, getattr(view, 'action', method.lower()), view.get_view_description())
+
+    def _get_description_section(self, view, header, description):
+        lines = [line for line in description.splitlines()]
+        current_section = ''
+        sections = {'': ''}
+
+        for line in lines:
+            if header_regex.match(line):
+                current_section, seperator, lead = line.partition(':')
+                sections[current_section] = lead.strip()
+            else:
+                sections[current_section] += '\n' + line
+
+        # TODO: SCHEMA_COERCE_METHOD_NAMES appears here and in `SchemaGenerator.get_keys`
+        coerce_method_names = api_settings.SCHEMA_COERCE_METHOD_NAMES
+        if header in sections:
+            return sections[header].strip()
+        if header in coerce_method_names:
+            if coerce_method_names[header] in sections:
+                return sections[coerce_method_names[header]].strip()
+        return sections[''].strip()
+
     def get_operation(self, path, method):
         operation = {}
 
         operation['operationId'] = self._get_operation_id(path, method)
+        operation['description'] = self.get_description(path, method)
 
         parameters = []
         parameters += self._get_path_parameters(path, method)
diff --git a/tests/schemas/test_openapi.py b/tests/schemas/test_openapi.py
index 78a5609da..0681833f8 100644
--- a/tests/schemas/test_openapi.py
+++ b/tests/schemas/test_openapi.py
@@ -71,7 +71,7 @@ class TestOperationIntrospection(TestCase):
         method = 'GET'
 
         view = create_view(
-            views.ExampleListView,
+            views.DocStringExampleListView,
             method,
             create_request(path)
         )
@@ -80,7 +80,8 @@ class TestOperationIntrospection(TestCase):
 
         operation = inspector.get_operation(path, method)
         assert operation == {
-            'operationId': 'ListExamples',
+            'operationId': 'ListDocStringExamples',
+            'description': 'A description of my GET operation.',
             'parameters': [],
             'responses': {
                 '200': {
@@ -102,23 +103,38 @@ class TestOperationIntrospection(TestCase):
         method = 'GET'
 
         view = create_view(
-            views.ExampleDetailView,
+            views.DocStringExampleDetailView,
             method,
             create_request(path)
         )
         inspector = AutoSchema()
         inspector.view = view
 
-        parameters = inspector._get_path_parameters(path, method)
-        assert parameters == [{
-            'description': '',
-            'in': 'path',
-            'name': 'id',
-            'required': True,
-            'schema': {
-                'type': 'string',
+        operation = inspector.get_operation(path, method)
+        assert operation == {
+            'operationId': 'RetrieveDocStringExampleDetail',
+            'description': 'A description of my GET operation.',
+            'parameters': [{
+                'description': '',
+                'in': 'path',
+                'name': 'id',
+                'required': True,
+                'schema': {
+                    'type': 'string',
+                },
+            }],
+            'responses': {
+                '200': {
+                    'description': '',
+                    'content': {
+                        'application/json': {
+                            'schema': {
+                            },
+                        },
+                    },
+                },
             },
-        }]
+        }
 
     def test_request_body(self):
         path = '/'
diff --git a/tests/schemas/views.py b/tests/schemas/views.py
index 273f1d30a..836a38016 100644
--- a/tests/schemas/views.py
+++ b/tests/schemas/views.py
@@ -29,6 +29,30 @@ class ExampleDetailView(APIView):
         pass
 
 
+class DocStringExampleListView(APIView):
+    """
+    get: A description of my GET operation.
+    post: A description of my POST operation.
+    """
+    permission_classes = [permissions.IsAuthenticatedOrReadOnly]
+
+    def get(self, *args, **kwargs):
+        pass
+
+    def post(self, request, *args, **kwargs):
+        pass
+
+
+class DocStringExampleDetailView(APIView):
+    permission_classes = [permissions.IsAuthenticatedOrReadOnly]
+
+    def get(self, *args, **kwargs):
+        """
+        A description of my GET operation.
+        """
+        pass
+
+
 # Generics.
 class ExampleSerializer(serializers.Serializer):
     date = serializers.DateField()