On a forum thread there is a button "Subscribe". This means that alert records will be created in Dynamics 365; however, the portal user/customer will receive no notification or pop-up when someone else adds a message or an answer to the forum thread.

It would be great if customers could easily be up to date with the latest messages of a portal. Customers may be subscribed to multiple threads at the same time and checking these regularly for updates can be time consuming. I suggest the following: push messages when you are logged in to the portal. You can enable these push messages by subscribing to a thread, and disable them by unsubscribing.