Thread: Heirs of Aragorn
They did for the most part. At least the northern kingdom was taken back and all the lands that previously belonged to Gondor. I remember reading this in the last part of the Return of the King.
Revendell, Lothlorien and all the other elven teritories were probably taken in the kindgdom as well, once all the elves left Middle Earth, this is not specified in the books I read, but I believe it to be true.