THE BACKSTORY OF THE HOBBIT AND SOME OTHER BITS
Thrain II, Thorin’s father, survived the Battle and he had a Ring of Power, you remember. His Ring was the last of the seven dwarf-rings that Sauron didn’t have and that hadn’t been melted in dragon-fire, and Sauron knew it, which is why Thrain’s family suffered so much, maybe? Most of the dwarves at the Battle of Azanulbizar assumed that Thror still had the ring, and had been wearing it when he went into Moria and died, and that part of what they were fighting for was to recover the ring from Azog. But no, Thrain had it all along.
Sauron’s plan with the seven rings was of course to make Dwarf nazgul, the same as the human nazgul, but it didn’t work — Dwarves are just too stubborn and intractable to be corrupted in that particular way. All the rings could do was make the Dwarves more Dwarfish: greedier, sterner, prouder. And so Thrain suffered from the same madness that had possessed Thror, and abandoned his family and went off to seek gold from Erebor or elsewhere with just a few retainers.
Somehow he ends up caught by Sauron and imprisoned in the dungeons under Dol Guldur, the fortress of “the Necromancer” (really Sauron) on the Hill of Sorcery at the southern edge of Mirkwood. The retainers go back to Thorin and tell him that Thrain is missing, presumed dead, and Thorin mourns and becomes king of his people, although he’s also a day laborer because there is no more kingdom.
Then one day he’s passing through Bree, and sees Gandalf, who’s just passing through on his way to the Shire, and Thorin flags Gandalf down and they have a conversation which eventually drives the entire plot of the Hobbit, which I don’t need to recount here.
Afterwards Dain becomes King Under the Mountain in Erebor, and as a much older Dwarf he fights orcs again during the War of the Ring, when Sauron tries to conquer the Lonely Mountain and Dale to use as a staging ground to drive off the Elves of Mirkwood. That campaign gets short shrift in the main text, but according to Tolkien here in Appendix A, if Dain and Bard the Bowman’s grandson Brand hadn’t led their people to battle against that host, there would have been “dragonfire and savage swords” in Rivendell and parts west and north.
Also, and this is about as random in the text as it seems here, a quick note about lady Dwarves: they’re outnumbered 2:1 by male Dwarves and non-Dwarves can’t tell them apart from male Dwarves (which is to say, beards, or else they bundle themselves up in the outside world such that you can’t see their faces under their hooded cloaks; this is a source of much nerdly dispute). Dwarves mate for life and sometimes not even then; if their chosen sweetheart rejects them and marries another, the rejected Dwarf is liable to remain celibate for life. Thus there are not very many baby Dwarves. Many Dwarves deal with this forced chastity by sublimating their lusts into gold-thirst and crafts.
One final note: after the War of the Ring, Gimli moves into the caves behind Helm’s Deep and builds a colony of Dwarves there, where he and Legolas are big ol’ pals, until much later when Aragorn dies of old age and Legolas decides to follow the rest of the Elves west across the sea, and he brings Gimli along; this means that Gimli is the only Dwarf to visit the Undying Lands, ever.
This concludes the remarkably textually dense Appendix A! The other Appendices are much less interesting to write about.