0101 originated from the combination of a self-replicating nanite swarm and Sentinel A.I. 0101 is never named in the actual issue it appears.
The mutant thief Gambit was hired by Olivia Trask to steal the nanites from Nanostorm, Inc. with the intention to use it for military applications and make a profit out of that.
When he learned of Olivia's intentions while delivering the vial containing the swarm, Gambit became suspicious of her and attempted to take back the vial.
The swarm was released when one of Trask's guards knocked down Gambit. The nanites interfaced with Trask's computer systems, and mutated into a Sentinel-looking humanoid figure. Thus, 0101 was born and ready to rampaging Manhattan.
The X-Men arrived to the scene and triend to stop the mad machine once they were alerted by Gambit. 0101 fled after Kitty Pryde used her phasing powers to disrupt its tech.
However, X-Men soon discovered that 0101 split apart, into smaller versions of itself, but was also targeting bystanders with any kind of mutation, from victims of cancer to mutants.
0101 seemed to be indestructible, but soon Prestige discovered that the machine was vulnerable to psychic attacks. Prestige attacked and managed to weaken the robot, but was knock unconscious by the latter. This effort allowed the X-Men to join forces with numerous other heroes in order to protect people from 0101. However, 0101 adapted to their attacks faster than they could hit it, and eventually overpowered them all, merging back into its humanoid and entire form afterwards. Neverthless, Prestige, who has recovered from her attack's backslash, attacked 0101, and destroyed once and for all most of the swarm.
0101 is presumed destroyed by Prestige's attack. However, at least one nanine, and possibly many, remained intact, which unfortunately went unnoticed.
Powers and Abilities
As an adaptive robot, 0101 was an extremely hard and formidable opponent for the X-Men, and it is one of most advanced Sentinels currently faced by the X-Men (a title which it shares with Nimrod, Master Mold and Bastion).
His nanite physiology, based on a nanite-physical structure, allows it a host of superhuman abilities such as shape-shifting (as long as he got nanites), nanite-dispersion and notably splitting itself apart at will. Thus, this allows him to perform extremely dangerous and deadly attacks, and makes him nearly unstoppable, as it is immune to physical weapons and injuries. Also, he has an adaptive artificial intelligence; being a Sentinel, it learns very quickly and evolves in response to every threats or obstacles he encounters, and can counter most attacks.
0101's only weakness is its inability to counter psychics attacks. In fact, it is very sensitive to that and it can be easily overpowered, providing that the psychic attack is enough strong to reach it.