The Alliance was the historic union of two former enemies, the Klingons and the Cardassians, in the face of aggression from the Terran Empire. The Alliance itself was led by a Regent, who delegated authority to various Intendants who administrated the individual sectors of Alliance territory. As of 2372, the Alliance was ruled by Regent Worf. The Alliance conquered the Terran Empire, following a series of reforms by Spock, the leader of the Empire, that left it vulnerable to attack. When the Alliance was finished, the Terrans were reduced to a slave race filling the mines of various Alliance planets.
The Bajorans became a major partner in the Alliance in the later 24th century, after their liberation from the control of the Terran Empire. However, the Bajoran rule would end up leading to one of the greatest threats to Alliance control.
On station Terok Nor, a bizarre accident in the Bajoran wormhole brought a Federation runabout from "our" universe into the mirror universe. The runabout's crew, Kira Nerys and Julian Bashir, were only aboard the station for a few days, but their presence incited a rebellion among the Terrans, led by Benjamin Sisko.
The Alliance tried (futilely) to crack down on the Terran Rebellion, but the rebels managed to elude the Alliance at almost every turn. Although Captain Sisko was killed by the Alliance in 2371, the rebels continued to fight on. By taking refuge in the Badlands, the rebels were able to avoid a confrontation with the Alliance fleet almost constantly.
In 2372, the Alliance suffered a humiliating defeat when the rebellion managed to capture Terok Nor. Regent Worf personally led the assault fleet that attempted to recapture the station, but that fleet was defeated thanks to a powerful new warship the rebels had hurriedly constructed.
As if the Terran Resistance Forces' initial victories were not humiliating enough, the Alliance suffered a further defeat during an operation in which Worf attempted to obtain a cloaking device from our universe. Regent Worf himself was captured along with the Alliance's flagship by the rebels and taken to Terok Nor in chains. (DS9: "The Emperor's New Cloak") The final fate of the Alliance after Regent Worf's capture is unknown.
While the Bajorans of the mirror universe have been influential members of the Alliance ever since the defeat of the Terran Empire, Kira Nerys has apparently been attempting to lead Bajor in rebellion against the Alliance. Her reasons for this are unclear, although it is most likely a simple power grab on her part.