Dwarves' Fate?

Elves sail to Valinor or are killed, and of the fate of Men, little is known besides that they die and go ...you know, wherever... Does Tolkien ever address what happens to Dwarves when they die? Or was that not allowed for, since Dwarves are not one of the original Children of Iluvatar but were made by a Valar? This is one of those small things that's going to bug me; if anyone knows the answer I would be grateful.