Temporal dissolution

Temporal erasure, (TV: Once, Upon Time) temporal dissolution, (PROSE: Timewyrm: Exodus, The Eight Doctors, World Game) or temporal excision, (PROSE: Engines of War) was the removal of an object or individual from time and space, as though they had never existed. This was a risk in changing history, (TV: In the Forest of the Night) sometimes as a result of the butterfly effect, (TV: Thin Ice) or otherwise due to unrestrained interference in the timelines, as during a large-scale conflict like the Last Great Time War. (AUDIO: The Starship of Theseus)

One could be erased from time by a time field, (TV: Flesh and Stone) or by technology used by the Time Lords and, during the Time War, the Daleks. (TV: The War Games, AUDIO: Neverland, PROSE: Engines of War) The Time Lords sometimes made a habit of "deleting" whole species from history, as a quick solution. (AUDIO: Fugitive in Time)

In some cases, time travellers could remember an individual even after they had been wiped from history, though the Eleventh Doctor explained to Amy Pond that she would not remember Rory Williams, as he was intimately linked to her own personal history. (TV: Cold Blood) On other occasions, the Doctor retained his memories of a previous timeline at least for a short while, while no one else did. Eventually, the Eighth Doctor's recollections of those erased from time in the Last Great Time War slipped away. (AUDIO: The Starship of Theseus, One Life) In many cases, the process, known as Time-fade, was gradual, with non-time travelers slowly losing their memories of an individual. (PROSE: Harvest of Time)

Time Lords
As far back as the Dark Times, the Division made use of temporal erasure options when deemed necessary. In the Siege of Atropos, the Time Lords supplied the Fugitive Doctor's operatives with temporal erasure technology. (TV: Once, Upon Time)

The Oubliette of Eternity, created by Rassilon, was employed by the Time Lords on those who committed high treason. Even Sentris, who had personally signed off on over 200 such "dispersals", did not recall after each act that anyone had been erased at all. Sentris dispersed herself when she found out. Ostensibly, when they were erased from the Web of Time, those affected ceased existing; in fact, they became Neverpeople. (AUDIO: Neverland)

The De-mat Gun was also capable of wiping its targets from time and space. This was termed "dematerialisation". During the Sontaran invasion of Gallifrey, the Fourth Doctor used the gun to eliminate Commander Stor and his unit of Sontarans. The De-mat gun was supposed to be forbidden knowledge, the existence of the gun known to all Time Lords who viewed it with horror. (TV: The Invasion of Time)

Tried for his crimes by the Time Lords, the War Lord was "dematerialised" out of existence along with his subordinate War Lords. (TV: The War Games) In an alternate universe, the War Lord was accidentally dematerialised out of existence along with his planet before the Time Lords could finish telling him that he would be dematerialised. (AUDIO: Exile)

As their most severe punishment the Time Lords were capable of throwing an individual's life-stream into reverse such that they would have never existed. By one account, they had intended this punishment for at the time of his arrival on Earth. (PROSE: Doctor Who and the Terror of the Autons)

The Celestial Intervention Agency was in the habit of "dematerialising" troublesome Time Lords to select for certain timelines. During the Last Great Time War, Narvin, Acting Coordinator of the CIA, spared some Time Lords from "dematerialisation" if he thought they might prove useful. This included the War Master. (AUDIO: From the Flames)

Later in the Time War, Rassilon wielded the Gauntlet of Rassilon, (AUDIO: Assassins) which possessed the ability to remove individuals from history. (PROSE: Engines of War) He used this power against the Partisan, reducing her to dust. He later intended to use his gauntlet against both and the Tenth Doctor, but ultimately failed to kill either. (TV: The End of Time) Following the war's end, Rassilon attempted to use the gauntlet against the Twelfth Doctor, but was stopped by the General. (TV: Hell Bent)

Last Great Time War
During the Last Great Time War, changes in reality caused Sheena to be renamed to Emma, then to Louise before disappearing from time entirely. (AUDIO: The Starship of Theseus)

Soon afterwards, Quarren, a Time Lord with a special ability to change reality with his thoughts, erased himself from time, and even the Eighth Doctor and his new companion Bliss soon enough could not remember him. Nevertheless, without even knowing why, the Doctor felt compelled to check up on Rupa Maguire, Quarren's wife. (AUDIO: One Life)

The Annihilator was a weapon designed by the Daleks during the Time War which erased whole species from time without affecting timelines. This meant that in the rest of the universe, those who had met them still remembered those lost, even though they no longer existed. The War Doctor pointed out that every member of a target race would feel themselves getting erased. The weapon was used by the Daleks on Vildar, erasing the Vildarans, and later by the War Doctor himself against the Technomancers. (AUDIO: Legion of the Lost) During the closing days of the Time War, the Dalek Eternity Circle constructed the Temporal Cannon, a weapon analogous to the De-mat Gun, testing it out on their human prisoners on Moldox. Harvesting three moons and the temporal radiation of the Tantalus Eye, the Daleks intended to fire this weapon at Gallifrey and erase it from existence only for the War Doctor and Borusa to destroy the Circle. (PROSE: Engines of War)

In an attempt to end the Time War, used the Heavenly Paradigm to alter the timelines, but inadvertently instead changed various planets' histories, largely for the worse. Among these worlds was Chelfrey, once a famed recreational planet, which ceased to exist as a direct result of the Master's actions. (AUDIO: The Heavenly Paradigm)

Post-Time War
After failing in her first attempt to ensure that her father did not die alone, Rose Tyler and the Ninth Doctor travelled back to a point just prior to his death in 1987, precariously close to their past selves. When Rose saved her father from the car that killed him, the past Doctor and Rose disappeared from existence. (TV: Father's Day)

Time field
Amy Pond's mother and father, Tabetha and Augustus Pond, were erased by the crack in her house. (TV: The Big Bang)

Aboard the Byzanitum, a crack erased several clerics of the Church. In quick succession, Crispin, Phillip, Pedro and Marco all came into contact with the crack and disappeared. Though the clerics were oblivious to what was going on, their memories of their lost colleagues being erased with them, Amy was able to remember them, having travelled through time. Soon after, the Eleventh Doctor used the ship's gravity to send the Weeping Angels, led by Angel Bob, falling into the crack. (TV: Flesh and Stone)

Shortly following his death at the hands of Restac, Rory Williams was erased from history when his corpse was consumed by the crack in the Silurian city. As Rory was a part of Amy's personal history, she quickly lost her memory of him. (TV: Cold Blood) However, Rory would later return as an Auton. (TV: The Pandorica Opens)

It was ultimately realised that the cracks in time had been caused by the destruction of the Doctor's TARDIS, which led to a Total Event Collapse. As the Doctor warned, this would cause every star to supernova at every moment in history, resulting in the entire universe never having existed. Further than that, a Cyber-Leader claimed that "all universes will be deleted." (TV: The Pandorica Opens) As the eye of the storm, Earth remained for a time, with the explosion of the TARDIS taking the place of the Sun. In addition stone after images of members of the Pandorica Alliance persisted, such as the Stone Daleks. In 1996 of the alternate timeline, the Eleventh Doctor used the Pandorica to reboot the universe in what he called Big Bang Two. As a result, Rory was restored to human form while Amy's parents returned as well. (TV: The Big Bang)

Other references
Speaking to Sarah Jane Smith in limbo, the Trickster contemplated using her to find and erase the Doctor, pondering "what chaos there would be across the stars" if they had never existed. (TV: Whatever Happened to Sarah Jane?)

When a solar flare threatened to destroy the Earth in the 2010s, the Twelfth Doctor explained to Clara Oswald that the many futures of Earth that they had witnessed through their prior travels through time would be erased should Earth be destroyed at this point. (TV: In the Forest of the Night)

When Bill Potts worried about potentially altering the future while at the 1814 Frost fair, the Twelfth Doctor jokingly told her that her friend "Pete" had just accidentally erased himself from existence after stepping on a butterfly on the corner of Blackfriars Bridge, and that Bill couldn't even remember him as a result. (TV: Thin Ice)