diff --git a/django/core/handlers/asgi.py b/django/core/handlers/asgi.py
index 021298e55d..bc9c2d76df 100644
--- a/django/core/handlers/asgi.py
+++ b/django/core/handlers/asgi.py
@@ -143,7 +143,7 @@ class ASGIHandler(base.BaseHandler):
         # FIXME: Allow to override this.
         if scope['type'] != 'http':
             raise ValueError(
-                'Django can only handle ASGI/HTTP connections, not %s'
+                'Django can only handle ASGI/HTTP connections, not %s.'
                 % scope['type']
             )
         # Receive the HTTP request body as a stream object.
diff --git a/tests/asgi/tests.py b/tests/asgi/tests.py
index 243e77defb..32520fae29 100644
--- a/tests/asgi/tests.py
+++ b/tests/asgi/tests.py
@@ -1,3 +1,4 @@
+import asyncio
 import sys
 
 from asgiref.sync import async_to_sync
@@ -82,3 +83,85 @@ class ASGITest(SimpleTestCase):
         response_body = await communicator.receive_output()
         self.assertEqual(response_body['type'], 'http.response.body')
         self.assertEqual(response_body['body'], test_file_contents)
+
+    @async_to_sync
+    async def test_headers(self):
+        application = get_asgi_application()
+        communicator = ApplicationCommunicator(
+            application,
+            self._get_scope(
+                path='/meta/',
+                headers=[
+                    [b'content-type', b'text/plain; charset=utf-8'],
+                    [b'content-length', b'77'],
+                    [b'referer', b'Scotland'],
+                    [b'referer', b'Wales'],
+                ],
+            ),
+        )
+        await communicator.send_input({'type': 'http.request'})
+        response_start = await communicator.receive_output()
+        self.assertEqual(response_start['type'], 'http.response.start')
+        self.assertEqual(response_start['status'], 200)
+        self.assertEqual(
+            set(response_start['headers']),
+            {
+                (b'Content-Length', b'19'),
+                (b'Content-Type', b'text/plain; charset=utf-8'),
+            },
+        )
+        response_body = await communicator.receive_output()
+        self.assertEqual(response_body['type'], 'http.response.body')
+        self.assertEqual(response_body['body'], b'From Scotland,Wales')
+
+    @async_to_sync
+    async def test_get_query_string(self):
+        application = get_asgi_application()
+        for query_string in (b'name=Andrew', 'name=Andrew'):
+            with self.subTest(query_string=query_string):
+                communicator = ApplicationCommunicator(
+                    application,
+                    self._get_scope(path='/', query_string=query_string),
+                )
+                await communicator.send_input({'type': 'http.request'})
+                response_start = await communicator.receive_output()
+                self.assertEqual(response_start['type'], 'http.response.start')
+                self.assertEqual(response_start['status'], 200)
+                response_body = await communicator.receive_output()
+                self.assertEqual(response_body['type'], 'http.response.body')
+                self.assertEqual(response_body['body'], b'Hello Andrew!')
+
+    @async_to_sync
+    async def test_disconnect(self):
+        application = get_asgi_application()
+        communicator = ApplicationCommunicator(application, self._get_scope(path='/'))
+        await communicator.send_input({'type': 'http.disconnect'})
+        with self.assertRaises(asyncio.TimeoutError):
+            await communicator.receive_output()
+
+    @async_to_sync
+    async def test_wrong_connection_type(self):
+        application = get_asgi_application()
+        communicator = ApplicationCommunicator(
+            application,
+            self._get_scope(path='/', type='other'),
+        )
+        await communicator.send_input({'type': 'http.request'})
+        msg = 'Django can only handle ASGI/HTTP connections, not other.'
+        with self.assertRaisesMessage(ValueError, msg):
+            await communicator.receive_output()
+
+    @async_to_sync
+    async def test_non_unicode_query_string(self):
+        application = get_asgi_application()
+        communicator = ApplicationCommunicator(
+            application,
+            self._get_scope(path='/', query_string=b'\xff'),
+        )
+        await communicator.send_input({'type': 'http.request'})
+        response_start = await communicator.receive_output()
+        self.assertEqual(response_start['type'], 'http.response.start')
+        self.assertEqual(response_start['status'], 400)
+        response_body = await communicator.receive_output()
+        self.assertEqual(response_body['type'], 'http.response.body')
+        self.assertEqual(response_body['body'], b'')
diff --git a/tests/asgi/urls.py b/tests/asgi/urls.py
index 4177ec8c9a..ff8d21ea7c 100644
--- a/tests/asgi/urls.py
+++ b/tests/asgi/urls.py
@@ -2,14 +2,23 @@ from django.http import FileResponse, HttpResponse
 from django.urls import path
 
 
-def helloworld(request):
-    return HttpResponse('Hello World!')
+def hello(request):
+    name = request.GET.get('name') or 'World'
+    return HttpResponse('Hello %s!' % name)
+
+
+def hello_meta(request):
+    return HttpResponse(
+        'From %s' % request.META.get('HTTP_REFERER') or '',
+        content_type=request.META.get('CONTENT_TYPE'),
+    )
 
 
 test_filename = __file__
 
 
 urlpatterns = [
-    path('', helloworld),
+    path('', hello),
     path('file/', lambda x: FileResponse(open(test_filename, 'rb'))),
+    path('meta/', hello_meta),
 ]