diff --git a/src/csharp/Grpc.Core/Channel.cs b/src/csharp/Grpc.Core/Channel.cs
index 2ec763bec152580e86c37eae70b538bae775d564..9cee7526630506a438af2e27e2d54e1ca058d35e 100644
--- a/src/csharp/Grpc.Core/Channel.cs
+++ b/src/csharp/Grpc.Core/Channel.cs
@@ -192,9 +192,16 @@ namespace Grpc.Core
         }
 
         /// <summary>
-        /// Waits until there are no more active calls for this channel and then cleans up
-        /// resources used by this channel.
+        /// Shuts down the channel cleanly. It is strongly recommended to shutdown
+        /// all previously created channels before exiting from the process.
         /// </summary>
+        /// <remarks>
+        /// This method doesn't wait for all calls on this channel to finish (nor does
+        /// it explicitly cancel all outstanding calls). It is user's responsibility to make sure
+        /// all the calls on this channel have finished (successfully or with an error)
+        /// before shutting down the channel to ensure channel shutdown won't impact
+        /// the outcome of those remote calls.
+        /// </remarks>
         public async Task ShutdownAsync()
         {
             lock (myLock)
diff --git a/src/csharp/Grpc.Core/Server.cs b/src/csharp/Grpc.Core/Server.cs
index 069185e13af9b6da2af5fee9ecaea1174d951d3f..6bd79005617e9347df44b34e23f6f30aa8086a01 100644
--- a/src/csharp/Grpc.Core/Server.cs
+++ b/src/csharp/Grpc.Core/Server.cs
@@ -152,6 +152,9 @@ namespace Grpc.Core
         /// cleans up used resources. The returned task finishes when shutdown procedure
         /// is complete.
         /// </summary>
+        /// <remarks>
+        /// It is strongly recommended to shutdown all previously created servers before exiting from the process.
+        /// </remarks>
         public async Task ShutdownAsync()
         {
             lock (myLock)
@@ -173,6 +176,9 @@ namespace Grpc.Core
         /// Requests server shutdown while cancelling all the in-progress calls.
         /// The returned task finishes when shutdown procedure is complete.
         /// </summary>
+        /// <remarks>
+        /// It is strongly recommended to shutdown all previously created servers before exiting from the process.
+        /// </remarks>
         public async Task KillAsync()
         {
             lock (myLock)