Very little is known about Abyss; he was first seen on the island of Genosha, where he was the bodyguard of the genoshan researcher Renee Majcomb, who was investigating the Legacy virus.
Later, he appeared in Berlin, fighting the mutant Fever Pitch who was trying to kidnap him. Abyss and Fever Pitch were both captured by the X-Corps, a mutant militia group founded by Banshee. Nils was held in a containment prison; from which he witnessed the death of Sunpyre, who was killed by Mystique. He then escaped from his confinement thanks to Banshee and to protect him; Nils sucked Mystique into the void within his body.
The next thing we know about Abyss is that he joined forces with Nightcrawler, his half brother, and the X-Men to stop Azazel from invading the Earth dimension with his army.
Abyss is a survivor of the Legacy Virus and was de-powered after M-Day. He recently joined a group of de-powered mutants known as the X-Cell. Abyss temporarily regained his mutation thanks to Pietro Maximoff. After seeing Elijah Cross die due to the side-effects of Quicksilver's unstable re-powering talents; Abyss took Fatale and Reaper and left for the Brimstone Dimension as he thought it may save them from exploding and losing their powers again. Abyss's fate is yet to be revealed.
Abyss's body unravels into high-tensile coils, and he possesses the ability to suck objects into the void in his chest cavity; sending them to another dimension.
The Abyss from the Age of Apocalypse was capable of sensing, and feeding off of, the fear of his opponents. It is not know if this Abyss, from Earth-616, is capable of doing that.
Age of Apocalypse Earth-295
In the alternate reality called Age of Apocalypse, Abyss is a wise-cracking egomaniac who wants nothing more than to impress his boss, Apocalypse. Not much is known about Nils' childhood. It is rumored that he was raised in Mr. Sinister's breeding pens. One day, he was able to break out; but instead of escaping, he murdered Bastion, one of Apocalypse's Horsemen of Apocalypse, in order to prove his devotion and willingness to rise to the top. Apocalypse was impressed and made Abyss his new Horseman in charge of the Southern Region of North America.
Abyss, along with the Madri and the Brotherhood of Chaos, attacked the site of a human evacuation in Maine. He introduced himself to the X-Men; consisting of Quicksilver, Banshee, Storm, Exodus, Dazzler, and Iceman. After murdering the Cardinal Madri for his failure to kill the escaping humans, Abyss revealed to Banshee that he has captured one the human children and is keeping him inside his body. He threatened to kill the child unless Banshee brought him Quicksilver, the son of Magneto. Abyss hoped to kill him in order to impress Apocalypse. Quicksilver complies and confronts the Horseman. During the fight, Quicksilver is able to wrap Abyss in his own coils, causing him to suck himself into his own dimensional void and disappear on the spot.
Abyss did not die, though, as he infiltrated the Madri Temple where Bishop was being interrogated by the Shadow King. Abyss believed that Bishop was extremely dangerous and a threat to Apocalypse's rule. Quicksilver, Banshee, and Storm attempt to rescue Bishop and are confronted with Abyss once again. In the ensuing battle, Banshee flied into the portal in Abyss' chest and let out a loud scream, blowing apart Abyss from the inside-out, but also killing himself in the process.
Abyss' powers in the AoA were the same as in the Marvel 616 Universe except he was capable of sensing, and feeding off of, the fear of his opponents.
Abyss appears as a boss to fight in the video game "X-Men Legends 2: Rise of Apocalypse". He is one of Apocalypse's Horsemen. After you defeat him, at the end of the fight he will transport all of your characters to the Brimstone Dimension.