diff --git a/README.md b/README.md
index 1e1d9e1..4477b76 100644
--- a/README.md
+++ b/README.md
@@ -41,28 +41,28 @@ class ExceptionToStatusInterceptor(ServerInterceptor):
     def intercept(
         self,
         method: Callable,
-        request: Any,
+        request_or_iterator: Any,
         context: grpc.ServicerContext,
         method_name: str,
     ) -> Any:
         """Override this method to implement a custom interceptor.
-         You should call method(request, context) to invoke the
+         You should call method(request_or_iterator, context) to invoke the
          next handler (either the RPC method implementation, or the
          next interceptor in the list).
          Args:
              method: The next interceptor, or method implementation.
-             request: The RPC request, as a protobuf message.
+             request_or_iterator: The RPC request, as a protobuf message.
              context: The ServicerContext pass by gRPC to the service.
              method_name: A string of the form
                  "/protobuf.package.Service/Method"
          Returns:
              This should generally return the result of
-             method(request, context), which is typically the RPC
+             method(request_or_iterator, context), which is typically the RPC
              method response, as a protobuf message. The interceptor
              is free to modify this in some way, however.
          """
         try:
-            return method(request, context)
+            return method(request_or_iterator, context)
         except GrpcException as e:
             context.set_code(e.status_code)
             context.set_details(e.details)
diff --git a/docs/index.rst b/docs/index.rst
index b410b68..ed2b556 100644
--- a/docs/index.rst
+++ b/docs/index.rst
@@ -77,31 +77,31 @@ To define your own server interceptor (we can use a simplified version of
        def intercept(
            self,
            method: Callable,
-           request: Any,
+           request_or_iterator: Any,
            context: grpc.ServicerContext,
            method_name: str,
        ) -> Any:
            """Override this method to implement a custom interceptor.
 
-            You should call method(request, context) to invoke the
+            You should call method(request_or_iterator, context) to invoke the
             next handler (either the RPC method implementation, or the
             next interceptor in the list).
 
             Args:
                 method: The next interceptor, or method implementation.
-                request: The RPC request, as a protobuf message.
+                request_or_iterator: The RPC request, as a protobuf message.
                 context: The ServicerContext pass by gRPC to the service.
                 method_name: A string of the form
                     "/protobuf.package.Service/Method"
 
             Returns:
                 This should generally return the result of
-                method(request, context), which is typically the RPC
+                method(request_or_iterator, context), which is typically the RPC
                 method response, as a protobuf message. The interceptor
                 is free to modify this in some way, however.
             """
            try:
-               return method(request, context)
+               return method(request_or_iterator, context)
            except GrpcException as e:
                context.set_code(e.status_code)
                context.set_details(e.details)
diff --git a/src/grpc_interceptor/server.py b/src/grpc_interceptor/server.py
index d399ac7..6cd6ebc 100644
--- a/src/grpc_interceptor/server.py
+++ b/src/grpc_interceptor/server.py
@@ -24,8 +24,8 @@ def intercept(
     ) -> Any:  # pragma: no cover
         """Override this method to implement a custom interceptor.
 
-        You should call method(request, context) to invoke the next handler (either the
-        RPC method implementation, or the next interceptor in the list).
+        You should call method(request_or_iterator, context) to invoke the next handler
+        (either the RPC method implementation, or the next interceptor in the list).
 
         Args:
             method: Either the RPC method implementation, or the next interceptor in
@@ -37,7 +37,7 @@ def intercept(
             method_name: A string of the form "/protobuf.package.Service/Method"
 
         Returns:
-            This should generally return the result of method(request, context), which
+            This should return the result of method(request, context), which
             is typically the RPC method response, as a protobuf message, or an
             iterator of protobuf messages for streaming responses. The interceptor is
             free to modify this in some way, however.
@@ -90,7 +90,7 @@ async def intercept(
     ) -> Any:  # pragma: no cover
         """Override this method to implement a custom interceptor.
 
-        You should call await method(request_or_iterator, context) to invoke the next handler
+        You should await method(request_or_iterator, context) to invoke the next handler
         (either the RPC method implementation, or the next interceptor in the list).
 
         Args:
@@ -103,7 +103,7 @@ async def intercept(
             method_name: A string of the form "/protobuf.package.Service/Method"
 
         Returns:
-            This should generally return the result of await method(request_or_iterator, context),
+            This should return the result of method(request_or_iterator, context),
             which is typically the RPC method response, as a protobuf message. The
             interceptor is free to modify this in some way, however.
         """