The final destination of the spirits of the deceased remains a mystery to the priests and philosophers of Azeroth. However, as spells such as [Resurrection] can reunite a dead body with its spirit, and a majority of living creatures from the tauren to the troll shadow hunters claim they can communicate with and call upon the power of the spirits, a widely held belief is that the spirits of the dead remain on the Material Plane — in an immaterial state that can only be altered or contacted through the use of magic.
Blizzard hasn't talked about what it plans to do after Shadowlands. I speculate that the longterm solution would be to do this every expansion—so in the next expansion, Blizzard might move Battle for Azeroth into the multitude of choices for new character-leveling experiences and push level-cap characters back down to 50 to start whatever expansion comes after Shadowlands—an odd hybrid of traditional MMO and a seasonal model common in plenty of modern multiplayer games.
Shadowy Tormentors inhabit this dimension, and emerge from it to torment death knights such as Koltira Deathweaver. The Lich King originally kept them at bay, but after the Knights of the Ebon Blade left his service, the tormentors are now loose upon them. He even appears in the World of the Dead, as he calls it, riding a frost wyrm during  The Power to Destroy.
The origins of the Shadowlands remain uncertain, but they have existed ever since mortal life first arose in the physical universe. They span all worlds, including Azeroth, on which Icecrown serves as an anchor to the Shadowlands. There are those who believe mortal souls are drawn into this dark place when they die, remaining there forever. Others hope their souls will go on to a brighter place rather than languish for eternity within the cold confines of the Shadowlands.