The Doctor's time stream

The Doctor's time stream contained all the Doctor's lives, all their deeds and memories, (TV: The Name of the Doctor) even those long forgotten. (TV: Once, Upon Time) As they led a complicated life, and made many enemies, who sometimes sought to have them come undone, the Doctor's time stream was subject to much manipulation. (PROSE: Unnatural History et al.)

Forces like Omega, (PROSE: The Infinity Doctors) the Great Intelligence, (TV: The Name of the Doctor) the enemy (PROSE: Unnatural History) and Faction Paradox (PROSE: Unnatural History, Interference - Book Two, The Shadows of Avalon) all played a part in rewriting the Doctor's biodata retroactively, making it so that even the Doctor's origins were contradictory and uncertain, with so many possibilities becoming true at once, in paradox. (PROSE: Unnatural History)

The Doctor visited their time stream on at least two occasions, once as the Eleventh Doctor on Trenzalore, to recover Clara Oswald after she entered to save the Doctor's past from the Great Intelligence, (TV: The Name of the Doctor) and a second time, in a bid to save Yasmin Khan and Vinder from a time storm in the fallen Temple of Atropos, as the Thirteenth Doctor. (TV: Once, Upon Time)

On this occasion, she had the opportunity to relive a long lost memory of her time as the Fugitive Doctor, near the end of her service to the Division. The Thirteenth Doctor nearly ended her life to stay longer, and find out what happened, but the Mouri threw her out. (TV: Once, Upon Time) This was also the space in which the Eleventh Doctor recognised — but still rejected — the War Doctor, who had scorned the name of the Doctor by deciding to destroy Gallifrey at the end of the Time War, (TV: The Name of the Doctor) though a different chain of events would soon be revealed. (TV: The Day of the Doctor)

Impact
As the Great Intelligence noted, the Doctor's time stream was a place of power, where many of the villains they had stopped might be given a second chance. (TV: The Name of the Doctor) As such, modifying the Doctor's history could lead to great catastrophe, with disasters they had once averted rippling out to become tidal waves. (TV: Turn Left, The Name of the Doctor) According to Clara, the Doctor could not help but have this impact, and became, himself, a "tidal wave" on history. (TV: The Girl Who Died)

In one case, the Doctor's time stream was "unravelled" without impacting the overall timeline of the universe, as the Eleventh Doctor found himself on the other side, in Big Bang Two. He began to re-experience moments in his life, moving backwards from the point of his sacrifice, and decided to end his journey where this incarnation began, on the day he met Amelia Pond. He would return, however, from Amy Pond's nascent memories. (TV: The Big Bang)

In another, one of the Doctor's companions, Donna Noble, was made to have never met the Tenth Doctor. This created "great, big parallel universe" in which the Doctor died defeating the Racnoss on Earth. (TV: Turn Left) In the original timeline, Donna was there to "stop [him]" from taking his rage too far. (TV: The Runaway Bride, Partners in Crime) Instead, a series of events led to the deaths of many allies and eventually, to the stars going out, (TV: Turn Left) as the Doctor and Donna were needed to stop the Reality Bomb. (TV: Journey's End)

History
At one point, when the Third Doctor was attempting to repair his TARDIS, he saw a brief appearance of other versions of himself, together with Jo Grant. When they disappeared, he told Jo they had gone "back into their own time stream". (TV: Day of the Daleks)

During the First Omega Crisis, Lord President Pandad IV, despite the objections of High Chancellor Socra, had the Second and First Doctors extracted from their respective sections of the Doctor's time stream to aid the Third Doctor against Omega. (TV: The Three Doctors)

Using a Time Scoop, Lord President Borusa took the first four incarnations of the Doctor and several of their companions out of their respective time streams again, to bring them to the Death Zone on Gallifrey. Here, they would play the Game of Rassilon on his behalf. In the case of the Fourth Doctor and Romana II, the attempt to lift them from the time stream was unsuccessful. They became trapped in a time eddy until the crisis was resolved. (TV: The Five Doctors)

During the crash of the Byzanitum, River Song acknowledged whilst speaking with Father Octavian that she was dealing with the Eleventh Doctor at an earlier point in his time stream, before he learned exactly who she was. (TV: The Time of Angels)

During Big Bang Two, the Eleventh Doctor experienced his own time stream "unraveling, erasing" and "closing" as he observed himself in the past. (TV: The Big Bang)

While awaiting his death at Lake Silencio, the Eleventh Doctor had the Teselecta send letters to Amy Pond and Rory Williams, River Song, Canton Everett Delaware III, and a younger version of himself. He explained that to deliver the messages himself, it would involve crossing his own time stream; "best not", he remarked. (TV: The Wedding of River Song)

The Doctor's time stream later appeared as an open wound in the fabric of reality inside the ruins of the Doctor's TARDIS in the future on Trenzalore, where the Doctor was buried. The Great Intelligence, in the form of Walter Simeon, arrived on Trenzalore, accompanied by faceless humanoids called the Whisper Men, whom he used to bring several of the Eleventh Doctor's friends there to draw him out so he could invade his time stream, turning all of his victories into defeats and having his ultimate revenge. He did so by directly entering his time stream inside the ruined future TARDIS. However, this plan was foiled by Clara Oswald, who followed the Great Intelligence through the wound. Just as he was, she was ripped into countless versions of herself throughout history and saved the Doctor countless times throughout his incarnations. The original Clara then found herself in a wasteland inhabited by various Doctors. The Eleventh Doctor entered the time stream and was able to extract her, though she saw an unknown incarnation. (TV: The Name of the Doctor)

The Twelfth Doctor, attempting to return to the Drum in 2111 from Краснодар in 1980, found himself half an hour back in time. Watching his earlier self arrive, the Doctor observed to Mason Bennett that he was now locked in his own time stream and so the TARDIS would not let him leave. As such, they had to stay out of sight before time caught up. (TV: Before the Flood)