Thousands of years ago, Omega was a highly intelligent solar engineer on Gallifrey. In the attempt to find and create a power source that would give the Gallifreyans mastery over time, he arranged the explosion of a star. The energy of the resulting black hole was harnessed, but according to Time Lord history, Omega was lost in the supernova. The remaining Gallifreyans became Time Lords and revered Omega as the greatest hero of their planet; but Omega had been blown out of existence into a black hole of antimatter, believing himself abandoned and forgotten when he should have been a god. His overwhelming desire for revenge has driven him quite mad. Omega is extremely emotional, although of course he also has a volatile temper, and not a lot of self-control.
Omega was able to survive in the antimatter universe through the force of his will. He is talented in psychosynthesis - the ability to create solid things from nothing using mental energy - and fashioned the world on which he lives in this manner, although it is unclear whether or not he is only able to do this in the antimatter universe. Bizarrely, Omega decided he wanted his world to look like a quarry. In his main complex is a lightstream that serves as a conduit into the regular universe; material travelling into the antimatter universe is converted from matter to antimatter. Omega's talents in psychosynthesis enabled him to create various living creatures, as well. Things are transferred between universes using a scout, a blob-like organism made of antimatter that serves as a time bridge, which causes things to disappear in a flash of light when it touches them. It can survive in both the matter and antimatter universes and imbues the same power to those it transfers. Omega also makes use of Gel Guards, tall creatures that appear to be made of amber bubbles with a single pink eye and claws that serve as weapons - light travels to the tip and causes an explosion wherever the claw is aimed. The Gel Guards serve as reinforcements, and are impervious to weapons. Another of Omega's experiments in psychosynthesis resulted in the Ergon, a tall avian/amphibian being that worked as Omega's servant.
Omega's first attempt to cross into the normal universe involved his using the scout organism to bring the Doctor into the antimatter universe, causing a cosmic energy drain on Gallifrey. Omega felt trapped in his antimatter universe because he was unable to transmit himself along the lightstream - it only existed while he was in the antimatter universe to maintain it with the force of his will. He wanted the Doctor to take over the task of maintaining the antimatter universe so that he could return to the normal universe. However, the Doctor was aware of Omega's resentment toward Gallifrey - Omega would be happy to destroy Gallifrey even if it eliminated all hope of his own freedom. In the end, questions of Omega's escape became moot - the corrosion from the lightstream had dissolved his body, leaving only his will behind, and he only existed at all because he had willed it so. His rage at discovering this led him to try to destroy everything, but in doing so, he also released a bit of unconverted regular matter - the second Doctor's recorder - into his universe, destroying it and the black hole.
Omega's next attempt to transfer himself to the normal universe involved stealing a fusion booster from Gallifrey and setting up a base in Amsterdam. His agent on Gallifrey was able to steal the Doctor's biodata extract, through which Omega wanted to bond with the Doctor, and Omega took control of the Matrix. His only desires were to have a life and to rest, but the bonding failed, and Omega decided that if he was to be denied life, then everyone else would die with him in the resulting explosion. Fortunately, the Doctor was able to destroy him before he could destroy the universe.