Since the appearance of the acerbic Sten in Dragon Age: Origins, the dogmatic Qunari have remained mysterious. As the series has progressed, so too has our knowledge of the Qun. The Qunari have become increasingly important as our conception of Thedas has expanded, as they provide an existential threat to the homelands of many Thedosians.
But, who are the Qunari? We have a wealth of knowledge of the history of Humans, Elves and Dwarves, but the Qunari's history remains conflicted and secretive. Before they adopted the Qun, the large humanoid race associated with the name 'Qunari' were known as Kossith. The first instance of the Qunari in Thedas was in -410 Ancient when a colony in the Korcari Wilds in southern Ferelden were captured by Darkspawn.
Almost 1,000 years later, the Qunari landed at Par Vollen, apparently arriving from a land across the Boeric Ocean. Iron Bull speculates the Qunari departed their homeland out of necessity, but concedes he doesn't know much else about the Kossith. That's about as much as we know officially about the origins of the Qunari.
In a Reddit thread speculating on horned statues that appear in the Raw Fade during the quest Here Lies The...