The Dalek Time Controller was a Dalek from the far future with a mind more capable of understanding time. It was strategist for time missions and fought various Doctors.
The Dalek Time Controller first met the Doctor during a plan to use the Cradle of the Gods to turn the 400 Sunlight Worlds into copies of Skaro. It manipulated the 11th Doctor into assisting with the plan, posing as the Dalek Litigator and prosecuting the Doctor for "hate crimes" against the Daleks, here the Daleks were viewed as benefical for setting up the Sunlight Worlds. However the plan was foiled when a Dalek puppet Jenibeth Blakely, turned on the Time Controller. However he escaped, nearly killing Blakely, though the Cradle of the Gods enabled her survival by reverting her back to childhood.
Amethyst Viral Containment Station
The Daleks traced viruses to the Amethyst Viral Containment Station and the Dalek Time Controller led a force to take the station through time. They met opposition from the Sixth Doctor. The Dalek Time Controller realised this was a time loop, an explosion would scatter the viruses through space and time which would lead to the Daleks tracing them back to the station. The Time Controller allowed the explosion to go ahead and the Doctor believed him destroyed in the explosion.
However the Dalek Time Controller was not destroyed, but hurled back in time to the late 22nd century, where the Daleks retrieved it. It was dying from temporal decay but the Meddling Monk was contacted by the Daleks and cured it. It planned another invasion of Earth, sending the Monk to spread another plague to weaken humanity, after which the Daleks invaded Earth again. North America was dug up and a Time Warp engine was installed. The Dalek Time Controller while in the vortex had found the point in the future where the Amethyst viruses would converge and planned to pilot Earth to that point, turning it into a plague planet, then pilot it round the Universe, infecting any world it came near to. However Lucie Miller sacrificed herself by crashing a Dalek Saucer into the mine, leading to the Daleks being dragged into a time warp.
However the Time Controller was saved by the Time Lord Straxus, who had become sick of the actions of the Time Lords and wanted to destroy them. The Dalek Time Controller altered his DNA, after which Straxus was known as Kotris. The Daleks invaded the planet Srangor and Kotris built a relativity map and temporal chamber to create a space-time projector, enabling them to see anywhere in space-time. Retro-genitor particles were implanted inside the human Molly O'Sullivan, who met the Eighth Doctor during WWI.
The Dalek Time Controller orchestrated chasing the Doctor and Molly through space-time. Finally Molly was captured on Srangor and the Daleks and Kotris tried to use the particles in her with the space-time projector to wipe out the Time Lords. However Kotris' previous incarnation, still called Straxus, had changed the particles in Molly so they would instead destroy the Daleks. When he told a local herder Molly would still die but for a nobler cause he stopped the process, unintentially saving the Daleks. The Time Controller then had Straxus exterminated, erasing Kotris and his actions from history, meaning Kotris didn't save him. However as the timelines shifted the Time Controller said he would remember this.
The Eighth Doctor met the Dalek Time Controller on Nixyce VII, a planet the Daleks had invaded. The Time Controller remembered the events with Kotris. The Doctor assisted the Time Controller against the Eminence, a gaseous race that were trying to conquer the Nixyce System and which he considered a greater threat then the Daleks.
The Dalek Time Controller, like all Daleks, was ruthless and devoted to the domination of the Dalek race. However it was more careful and patient then most Daleks due to its greater understanding of time, not wanting to cause destabilisation in the Web of Time that could ultimately harm the Daleks. It didn't immediately exterminate the Sixth Doctor due to space-time protocals. It didn't exterminate the Eleventh Doctor so he could be manipulated into enabling the activation of the Cradle of the Gods.