Kingdom of Ivalice
No dwarves; the only downside of having a human-only campaign.
But, the dwarven stereotype lives on in the sturdy mountain-folk of the northeastern Duchy of Zeltennia. Either that or the Russian stereotype. Or is it the Rokugan Crab Clan stereotype? Anyway, dwarves are sort of Russian in their habits and the Crab Clan were even shown as dwarves in the alternate Rokugan option in OA, so I hold that their stereotype lives on.
Dwarven Age
Stereotypical dwarven culture is like a mix of Anglo-Saxon, Confucian Chinese and Imperial British. If that recipe isn't going to dominate the entire world, I don't know what will. Add the fact that dwarves are now pretty much the most effective race on average of any of the core races and you have the recipe for world domination.
Such is the case in the Dwarven Age. Emerging in the last millennia, the high dwarves (PHB dwarves) swept aside the allied kingdoms of men and orcs and the remnants of the elven empire those luminaries ousted. The dwarves were few in number, being a young race, but they bred fast, lived long, and took a great deal to kill. They were also natural inventors, merchants and soldiers.
The dwarven race has two older, smaller subraces, the physically weak but mentally agile low dwarves (PHB gnomes) and the unintelligent but tough cave dwarves (OA korokoboru). The high dwarves grant these lessers higher status than any non-dwarven race other than giants (see below), but still keep them under control.
These industrious, imperialistic high dwarves descend from matings between the lesser dwarven races with scattered giants (AU giants), who fled underground after losing a long war with the elves. Although not citizens, the remaining giants are still accorded respect by their dwarven descendants for their age and wisdom.
The high dwarves are split into two great nations: a constitutional monarchy and a mercantile oligarchy. The former is largely benevolent in its imperial rule, treats the "lesser" races like humans and orcs kindly, and allows low and cave dwarves to rise to positions of authority if they prove their mettle. The latter is ostensibly open and encourages lesser race trading partners, but imposes brutal industrial slavery on those within its borders. A third faction, promoting full dwarven equality and the purging of the tainted lesser races, has established a foothold as well, led by a charismatic schemer, a dwarven cross between Lenin and Hitler.
All three factions control powerful steampunk-level technology, but have little aptitude for magic.