First Omega Crisis

The First Omega Crisis was the incident in which Omega returned to threaten Gallifrey for the first time. (TV: The Three Doctors) It was followed by the Second Omega Crisis. (TV: Arc of Infinity, PROSE: A Brief History of Time Lords)

The First Omega Crisis notably marked the end of the Third Doctor's exile on Earth. (TV: The Three Doctors)

Dating
The Third Doctor's exile, as recorded by Kadiatu Lethbridge-Stewart, lasted for five straight years in the 1970s. (PROSE: Transit) He had first appearanced on Earth, having recently regenerated, some months following the first Cyberman invasion, which itself took place four years after the London Event. (TV: Planet of the Spiders, The Invasion)

The Crisis
After thousands of years in the void, Omega hit upon a plan of revenge: a captured Time Lord could be forced to take his place, and Omega could leave and wreak vengeance on Gallifrey. This plan was inspired by the Verdigris, who had travelled into the anti-matter universe in an attempt to get the Third Doctor released from his exile on Earth. (PROSE: Verdigris) Using the black hole, he drained power from the Time Lords to stop them from interfering. He sent an amorphous life form and other, more humanoid servitors to find the exiled Third Doctor and take him into the black hole. The High Council, unable to send anyone to assist the Doctor, decided to have the second incarnation of the Doctor help rectify matters, subsequently contacting and sending his first self to advise them. Omega brought both incarnations to his domain, entry into which converted all matter into anti-matter.

When Omega removed his helmet to prepare for his departure, he discovered that the anti-matter universe had completely dissolved his physical body. He could not leave his universe; he existed only because his will insisted that he exist, but his will was all that was left of him. Consumed by rage and despair, Omega swore to destroy all things. The Doctors offered freedom to Omega: in actuality the Second Doctor's recorder which the Doctor's TARDIS had accidentally shielded from conversion into anti-matter. The Doctors attempted to trick Omega into touching the recorder but instead only infuriated him. When Omega lashed out he knocked the force field generator to the floor, causing the recorder to make contact with the floor and creating a violent matter-antimatter explosion which seemingly killed Omega, collapsing the antimatter world. (TV: The Three Doctors)

Aftermath
As a reward for the successful defeat of Omega, the Time Lords finally rescinded the Doctor's exile on Earth, granting him his lost memories as well as a brand new dematerialisation circuit to restore his TARDIS to working order. (TV: The Three Doctors) Despite his exile coming to an end, the Doctor continued to work with UNIT on a regular basis and retain his home base there for the remainder of his third incarnation. Following his regeneration, however, the new Doctor finally took full advantage of his freedom and quickly weaned himself away from UNIT, save for the occasional collaboration, (TV: Robot, Terror of the Zygons, The Android Invasion, etc.) and also took part in adventures on Earth on a less-frequent basis than he had done previously, although he never officially resigned from UNIT. (TV: The Day of the Doctor)

At a UNIT reunion, the Second Doctor and the Brigadier reminisced about the Yeti, the Cybermen and Omega, with the Brigadier observing that they had "seen some times". (TV: The Five Doctors)

Omega survived the explosion, but became trapped in a crimson bubble of time. He began taking spacecraft into his realm, including the Rigelian Seventh Fleet, the disappearance of which was investigated by K9 Mark I. Now calling himself Omegon and claiming that the Time Lords had made him Emperor and then betrayed him, he used the thousands of spaceships he had collected to launch an attack on Gallifrey to get his revenge. However, K9 launched his spacecraft K-NEL at the rocket stores of Omegon's flagship, destroying it in a colossal explosion which seemingly killed Omegon. (PROSE: K9 and the Time Trap)

Behind the scenes

 * John Dorney's original ending of Return of the Cybermen explained that many aspects of the Doctor's personal timeline were being rewritten by the fallout of Genesis of the Daleks and the Last Great Time War. These changes included "the meeting of [his] three previous selves go[ing] very differently", suggesting some alterations to the Omega Crisis. The scene was ultimately cut from the script and not recorded.