The Shi'ar Empire is a relatively ancient collection of worlds and civilizations, culturally and politically "married" together under the overall control of the original Shi'ar race, the bird-like people of the Aerie. The Shi'ar are ruled by a hereditary bloodline of Majestors and Majestrixes, traditionally from the Neramani family line. They have an army of champions known as the Imperal Guard, staffed by superhumans and elite soldiers culled from the dozens of species in the Imperium.
The insane Majestor D'Ken ruled the Shi'ar when they were first introduced, from X-Men (1st series) #97-109. After D'ken was driven into a catatonic state by the M'Kraan Crystal, his younger sister Lilandra rose to the throne, and officially assumed the rank of Majestrix after #114. She took the Earthman Charles Xavier as her royal consort. Lilandra was deposed by her elder sister in exile, Deathbird, in #154-162, and the eldest Nermani sibling remained in power until #275.
Lilandra's second term of rule over the Shi'ar Empire led to a successful war with the Kree, who surrendered and were forcibly annexed into the Shi'ar Empire between the crossovers of Operation: Galactic Storm in 1992 and Maximum Security in 2001. The Shi'ar Empire suffered greatly at the hands of Cassandra Nova in New X-Men (1st series) #122-126, as she vented her rage against Charles Xavier through Lilandra and her people, leaving the Majestrix mentally disabled for a time.
In the Rise and Fall of the Shi'ar Empire from Uncanny X-Men #475-486, D'Ken briefly returned for a coup against Lilandra's failing reign before being killed in turn by Vulcan, newly crowned member of the royal family and husband to Deathbird. As Emperor Vulcan, the former X-Man led the Shi'ar into a costly War of Kings, attacking many nearby civilizations and entering a second war with the Kree Empire, which they ultimately lost. With Lilandra and Vulcan dead by the end of the war and Deathbird comatose, Gladiator rose up from Praetor of the Imperial Guard to acting Majestor, as the Shi'ar Empire was surrendered fully to Kree control.
