We Know Elves Were Gone, but What Happened to Dwarves After LotR?
Did the dwarves follow the elves into the undying lands, or did they just dig their way out of Middle-earth?
In The Lord of the Rings, it was always said that with destruction of the One Ring the time of elves will end, the remnants of their glory will fade, and the survivors of their race will have no choice but sail to the West, never to return, as the weight of passing time will press increasingly heavily on those who remain in Middle-earth.
And so it happened.
With the final defeat of Sauron, the Fourth Age of Middle-earth, also known as the Age of Men, had finally begun, and while some elves still lingered for a time, their days in Middle-earth were clearly past.
But what happened to dwarves, then? Well, the dwarven people flourished at first, will all the menaces which threatened them for millennia – the balrog, fire-breathing dragons, Sauron – now gone. Gimli and his fellow dwarves of Erebor and the Lonely Mountain helped to rebuild Gondor after the war, better than it was before.
Gimli himself even founded a new Dwarven kingdom, located inside the caves under the Helm's Deep (the beauty of these caves and Gimli's delight upon discovering them is omitted from the movies). Going by Tolkien's Unfinished Tales, the greatest dwarven kingom in Moria was restored as well: King Durin VII the Last eventually retook Khazad-dum, and made it as great and magnificent as it once was. All in all, dwarves did pretty well, at least for a time.
But that time was not to last forever, though we have no indication how long that new golden age of dwarves was supposed to be. Eventually, as Unfinished Tales continue, "The world grew old and the days of Durin's race ended."
There are no further details about this sad outcome for an entire race. But The Lord of the Rings was always supposed to be a work of mythology, taking place before the history of real-life Earth timeline, as we know it, so something like this was inevitable.
The Age of Men implied gradual extinction of fantasy creatures and races, but given timescales of Middle-earth, for dwarves the road to that extinction could have taken longer than our entire real-life written history.