Post-Time War universe

At the cessation of the Last Great Time War's main conflict, the constant shifting timelines which had defined the war resolved into a single version of the Doctor's universe (PROSE: Dalek: The Astounding Untold History of the Greatest Enemies of the Universe, The Paradox Moon) into which the Ninth Doctor survived (TV: Rose, The Unquiet Dead, et al.) and the Tenth Doctor continued to exist in. (TV: New Earth, Journey's End, et al.) As the Doctor's life continued into his next incarnation, the universe would be rewritten by the total event collapse, nearly dying in its final form as the Starless World before being recreated as a rebooted universe. (TV: The Big Bang)

Origins
During the Last Great Time War, this reality was observed as a Matrix extrapolation of the possible future. (PROSE: Dalek Combat Training Manual)

The creation of this reality involved the wiping out of a trillion other timelines. (PROSE: He's Behind You) The time lock sealed off the fighting of the Time War, (TV: Journey's End, COMIC: Don't Step on the Grass) While sources would indicate the Time War ended in Gallifrey's destruction, (TV: The End of the World, COMIC: Don't Step on the Grass, PROSE: Doctor Who and the Time War) numerous incarnations of the Doctor would later change history without changing the Ninth and Tenth Doctor's lives so that Gallifrey secretly survived. (TV: The Day of the Doctor, PROSE: Dalek Combat Training Manual, COMIC: The Good Companion, et. al) Some accounts even suggested this was not a change to the timeline at all, which would mean Gallifrey had in fact always been saved and that the Doctor simply had been unable to remember it. (PROSE: The Day of the Doctor, et. al)

General outline
At the end of the Ninth Doctor's life, Rose Tyler looked into the heart of the TARDIS and become the Bad Wolf entity. She then used her seemingly unlimited reality-warping powers to spread the Bad Wolf meme throughout space and time, so she would reach that moment (thereby creating an ontological paradox). (TV: The Parting of the Ways)

Into the Tenth Doctor's life, Dalek Caan manipulated the timelines to ensure a version of reality where the Doctor and Donna Noble travelled together and eventually created the Doctor-Donna to stop Davros' reality bomb. Caan believed that this would always have happened, and that he'd "only helped". (TV: Journey's End)

Fate
Near the end of the Doctor's time with Donna, a complicated tangle of events centralized in the Eleventh Doctor's lifetime began intersecting with the Doctor's present. (TV: Silence in the Library, The Time of the Doctor) Into the beginning of the Eleventh Doctor's life, cracks in time erasing the universe, creating a dwindling incomplete reality in which many pieces of the Tenth Doctor's reality no longer existed. (TV: Flesh and Stone, The Pandorica Opens) Reality was nearly completely destroyed save for a momentary Starless World, but the Doctor was able to use a few surviving particles from the original reality to initiate a Big Bang Two to create a rebooted version of the post-Time War universe. (TV: The Big Bang)

Relation to other realities
When the Eighth Doctor of the post-War universe looked into his further future in a Tomorrow Window, this timeline emerged as the dominant potential reality. However, other parallel potential realities included (PROSE: The Tomorrow Windows) one where a different Ninth Doctor planned on marrying his companion Emma. (PROSE: The Tomorrow Windows, TV: The Curse of Fatal Death) Marnal investigation of the temporal complexity around the Eighth Doctor found that it continued into the Doctor's ninth incarnation, with the Eighth Doctor's timeline non-linearly leading to three different Ninth Doctors. (PROSE: The Gallifrey Chronicles)

Due to a Time Beetle, this universe once branched into Donna's World. (TV: Turn Left)

Continuity with other versions of reality
The Ninth Doctor actively remembered having three parallel lives before the Time War: one where he travelled with Sam Jones, one where he travelled with Charley Pollard, and one where he travelled with Izzy Sinclair. The Doctor remembered these lives as "happy jumbled days" which coalesced into the War Doctor's life and remained in the Doctor's past following the Time War. (PROSE: The Eighth Doctor Part 2)