From : Gallifrey
[The Third Doctor describes Omega as a hero to the Time Lord's] "I generated those forces... and for what? To be blown out of existence into this black hole of Anti-matter.... A hero? I SHOULD HAVE BEEN A GOD!" Omega - The Three Doctor's 1973.
Omega was the one of the original founding fathers of the Timelord empire, along with Rassilon.
He was a Stellar Engineer who created a device known as the "Hand Of Omega" which could manipulate star matter. This was to provide enough power to undertake time travel experiments, along with Rassilon.
One of these time travel experiments went Supernova and Omega was apparently killed as he and the experiment collapsed into a black hole.
It was Rassilon who followed up on Omega's research and tamed the power source, converting it into the 'Eye Of Harmony' - the Timelord's power. Rassilon then became Lord President of Gallifrey.
Omega hadn't died but had been thrown into an alternate anti-matter Universe, where he plotted his return to the matter Universe.
In The Three Doctor's - 1973, Omega (who had gone quite insane) had found out how to strike out of his anti-matter prison at the matter Universe. The Timelords, believing the threat to be serious; allowed the Third Doctor to summon both of his previous incarnations to aid him. Drawn into the anti matter Universe they meet Omega who intends to use them to trade places and escape his anti-matter prison, leaving them stuck in it.
The Doctor's explain to Omega that he couldn't return as he doesn't have a physical form anymore. After removing his helmet, Omega is shown as having no form at all.
The Doctor's manage to escape by offering Omega a device they say will allow him to escape but it contains a "matter" version of the Second Doctor's recorder, which explodes on impact with the anti-matter Universe sending the Doctor's back and seemingly "killing" Omega.
Omega was back in Arc Of Infinity - 1983 for another shot at returning to the matter Universe. This time, using the guise of a anti matter creature known as 'The Renegade' and in league with rogue elements of the Time Lord high Council; Omega steals the Fifth Doctor's bio data which means he can create a double of the Fifth Doctor and possess its body.
Materialising in Amsterdam on Earth, Omega heads off in his new body to fulfill his senses in the matter Universe, with the Real Fifth Doctor in pursuit. Omega's Doctor duplication begins to fall apart and the Fifth Doctor catches up with Omega before dispatching him back to his anti-matter prison.
And that is where he has stayed since, I have no douby though that the 'greatest hero of the Time Lord's' will be back in the new series at some point. Until then he stays in his anti-matter prison wiling away his time, plotting the Doctor's downfall.