Genosha used to be a hellish place on the Earth. It was nice for a short amount of time, and it was then reduced back to a hellish place. Only through a lot of work and perseverance will it stand tall-and it won't be easy.
For most of Genosha's time, it was an island off the east coast of Africa. Its capital was Hammer Bay. At a glance, it seemed to be a good, prosperous nation. The standard of living was high and the citizens were well-treated. The economy was excellent and growing all the time. Political or racial turmoil was non-existent. Good things seemed to be happening in little Genosha. But all these things only applied for the humans of this small, inconspicuous, seemingly unimportant island nation.
In Genosha, the mutant population was enslaved. David Moreau, a scientist was known as the Genengineer. Anyone with the mutant gene was forced through a horrific treatment developed by the Genengineer. They were genetically modified and enhanced for their powers, and stripped of free will. They were treated like animals and given numbers, identified by those numbers. Their powers were changed to fit the needs of the economy. Then they were shipped off and worked as slaves until they died. No one was allowed in or out of Genosha. If you are a citizen, you will stay a citizen until you die. If you are not a citizen, then you're not getting in Genosha. The Magistrates were a special police force that tracked down people who tried to escape and brought them back forcibly, and the Press Gang handled mutant problems. All in all, it was a horrible place.
The island of Genosha was often an enemy of the X-Men and other teams in the Xavier Institute (including X-Force, X-Factor, and Generation X). Since mutants are horribly treated there, they often go to rescue the poor people, and Magistrates often attack them to bring them into Genosha, Wolverine, Rogue, and Madelyne Pryor were kidnapped by Magistrates under the orders of the Genengineer and Cameron Hodge. Hodge used to be an ally of X-Factor, but he became a mutant hater. They were rescued, though. Later, Wolfsbane and Storm were kidnapped and going to brainwashed to be Genoshan "citizens". The X-Men freed their compatriots and toppled the Hodge and the Gengineer's regime. The new government promised kindness and humane treating of mutants, but spurred on by the Fabian Cortez, Civil War broke out between the Mutates and Magistrate forces.
Magneto's Regime and the Fall of Genosha
After Cassandra Nova's Attack
Playing on his reputation, Magneto made his last blackmail attempt on the world threatening to destroy planetary EM field if he was not granted territory to create a mutant homeland. Despite the efforts of the X-Men to stop him, including the ultimate sacrifice of Magneto's clone Joseph, the U.N. granted Magneto Genosha. The island nation had been torn apart by civil war between the Magistrate regime and the Mutate rebellion for months (perhaps years) and the U.N. hoped Magneto would be so bogged down in fighting this war, the Legacy Virus sweeping through the population, and Genosha's failed economy that he would never trouble the world again.
They were wrong. Within six months, Magneto had led the mutants and mutates to victory, and the Legacy Virus was cured. Magneto quickly rebuilt Genosha into a prosperous mutant paradise. Overconfident, Magneto declared war on humanity again. The X-Men snuck into Genosha to intervene and in the course of battle, Magneto's spine was severed by Wolverine. As Magneto's powers are dependent on his nervous system being intact, this not only left him paralyzed but unable to use his powers. This event would end up costing millions of lives.
In revenge for Xavier's mistreatment of her, Cassandra Nova found the last living relative of Bolivar Trask, who had created the Sentinels. She then convinced him to give her control over the Sentinels. She sent them them to Genosha where they began wiping out the population. Depowered, Magneto was unable to stop them. The entire island was reduced to a pile of rubble, and all the progress was lost. 16 million people were killed, leaving perhaps a couple hundred survivors. Nova was eventually defeated by the X-Men back in New York, but the damage was done.
Magneto and Professor X joined forces to reform Genosha, but their work was interrupted by the Scarlet Witch's nervous breakdown and the events of House of M. In the world of House of M, Geonsha was Magneto's seat of powers, and therefore the most prosperous nation in the world. However, when Wanda revered the world to normal, not only was Genosha restored to it's decimated state, but her entire mutant population, including its leader, was turned into normal humans. SHIELD eventually removed the last of the Genosha population for medical treatment, but Magneto remained. When they attempted to remove an unconscious Magneto from Genosha after his and the Avenger's encounter with the Collective, Magneto escaped.
Whether Magneto retains legal possession of Genosha is unknown.
Selene's plans involve resurrecting the millions of dead mutants on the island and to make it the start of her kingdom.
Through unknown means Apocalypse managed to convince The Celestials that Genosha was a threat to Mutantkind much like The Deviants had been a threat to Humankind and so, like Lemuria before it, Genosha was obliterated by Arishem the Judge and his Host. While much of its population managed to escape, not all of Genosha's inhabitants were fortunate enough to escape the wrath of their Celestial creators.
Ultimate Genosha is a small island south of Madagascar. It mostly does television programs, and the Ultimate versions of Longshot and Mojo live there. It seems to be crossed between Earth-616 Genosha and the Mojoworld, as mutants are only second-class citizens there.