A similar entry appears in the Wheel of Time Companion confirming the information available in the main story arc.
Unless stated otherwise, all information herein is taken from The World of Robert Jordan's "The Wheel of Time", Chapter 17.
Much of the history of the land of Seanchan is obscure and unknown, but there are details that are known to us.
After the Breaking, the society in the Seanchan lands collapsed in much the same way as throughout the rest of the world. The land was in constant warfare, with short lived alliances between nations breaking or forming over the course of the many wars. Despite this lack of stability, the Seanchan were able to almost entirely eradicate Shadowspawn from their lands during the course of the first thousand years after the breaking (TWoRJTWoT, Ch. 18). It was during this period that the Seanchan exotics were first brought from lands beyond the Portal Stones. Women who could channel, calling themselves Aes Sedai often fought in these wars and the armies that Luthair found, featuring Aes Sedai and strange powerful beasts, became known as the Armies of the Night.
Luthair was able to use the shifting alliances and mistrust the Seanchan felt for each other to conquer much of the land. In this, he was also helped by his use of damane, which the other nations did not possess, the first a'dam having being made for him by Deain. Luthair himself did not complete the conquest, which was affected over almost three hundred years, with a further two hundred to finally remove any formal opposition, in a period known as the Consolidation.
Many of the aspects of Seanchan culture, such as the keeping of da'covale and the very strict class boundaries were features of the original nations that made up the continent and were absorbed into Luthair's empire over time. Similarly, the Crystal Throne is unlikely to have been taken to Seanchan with Luthair.