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
Having lost his memory of the fall of Gallifrey, (TV: The Day of the Doctor) the Ninth Doctor believed that both the Time Lords bar himself and the Daleks had been wiped out, to the point that he initially took the sight of a Dalek on Earth in 2012 to be "impossible". This lone Dalek survivor, who was skeptical as to the Doctor's account of the war's end, searched for traces of its kind by scanning Earth's internet, satellites and radio telescopes, only to find "nothing". (TV: Dalek) Similarly, the Tenth Doctor was hesitant to consider that Yana, actually, was a disguised Time Lord, insisting that they had all died. (TV: Utopia)

In fact, humanity at the time of the Dalek Emperor's return in the year 200,100 knew of the Daleks, but understood that they had all disappeared thousands of years prior. Jack Harkness, a 51st century Time Agent, noted that the Daleks were "the greatest threat in the universe" before their sudden disappearance, which the Ninth Doctor confirmed was so they could fight the Time War. (TV: The Parting of the Ways) Jack, who recognised the bronze Dalek saucers, originally believed that they had been destroyed (TV: Bad Wolf) and that the Time War was just a legend. (TV: The Parting of the Ways)

To the rest of the universe, the Daleks and the Time Lords had become creatures of legend, ancient races that had obliterated one another. The surviving higher species rejoiced, free at last from the conflict that had threatened their very existence. (PROSE: Dalek: The Astounding Untold History of the Greatest Enemies of the Universe)

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)

Sarah Jane Smith, companion to the Third Doctor in the Exxilon Incident (TV: Death to the Daleks) and the Fourth Doctor in the Genesis Incident, (TV: Genesis of the Daleks) remembered the Daleks following her travels in the TARDIS (TV: School Reunion) and was later embroiled in the invasion of Earth by the post-war New Dalek Empire. (TV: The Stolen Earth/Journey's End) Alistair Gordon Lethbridge-Stewart, who led UNIT forces in the Time Paradox Incident, (TV: Day of the Daleks) recalled his encounter with the Daleks following the aforementioned invasion. (TV: Enemy of the Bane)