Diablo III: Reaper of Souls

As for the Realm of Trials...that was where you fight a bunch of spawns to determine the level of your Greater Rift Stone, right?

Yes, that's correct. I used to spend hours just converting my trial keystones. The only feature they showed so far about this new change is that it has a drop-down menu on which Greater Rift level you'd like to do. I still don't know exactly how it works so we'll see.