Cyberverse
The "Cyberverse", as Reece Goddard called it, was an alternate timeline in which the Cybermen became a dominant force in the universe. Its very existence was a temporal paradox.
At some point in the far future when the Cyber-Fleets were destroyed and the Cyber-race nearly wiped out, the Cyber-Controller discovered the water planet Chronos, killed the inhabitants, and gained access to their time travel portal and its control device, the Chronosphere. Although he could not pass through the portal without his non-organic parts being erased, he reached back to the planet in 3286 when the Sixth Doctor was there.
As a nexus point, in an alternate 3286, the Doctor gave the Cybermen the TARDIS for infinite access to time and space. Using this, they travelled back to Earth in 1927 and released a techno-organic virus that converted most humans into techno-organic beings. A retro virus was used to create more advanced Cybermen known as "skin drones" where they were completely cyberised apart from their skin and brains. The Cybermen spread across other divergent timelines from here, and by 1951 the Time Lords, Daleks, Sontarans, and Draconians had all been conquered.
Reece Goddard, a 1300 year old skin drone, used the Chronosphere to travel to the nexus point and prevent the Doctor giving the Cybermen time technology. He brought with him the virus, having reverse-engineered it into an organic-techno virus that would attack the Cybermen's mechanical parts, turning them to goo. The Doctor, however, realised that the Cybermen would reverse-engineer the virus themselves and create the techno-organic virus from there, the virus' existence being a paradox.
The Controller infected Evelyn Smythe with the virus, although the results of this were never seen. Upon killing it, Goddard discovered the Controller had been a future Evelyn. (WC: Real Time/AUDIO: Real Time)
Relation to other realities
During his multiversal adventure, the Sixth Doctor saw a version of himself who travelled with a partly-cyberized Evelyn Smythe. (PROSE: Spiral Scratch)
