Final End

The Second Doctor initially believed the Civil War in the Dalek City to be the "Final End". (TV: The Evil of the Daleks)

The Final End was the hypothetical extinction of the Dalek species as pondered by human historians. (PROSE: Dalek: The Astounding Untold History of the Greatest Enemies of the Universe)

History

The Second Doctor observed the "final end" of the Daleks as the Dalek Civil War raged in the Dalek City on Skaro, with Daleks loyal to the Dalek Emperor engaged against the Humanised Daleks the Doctor had created. (TV: The Evil of the Daleks) Human historians were aware of his use of the term but were also aware, as he would later learn, (PROSE: Dalek: The Astounding Untold History of the Greatest Enemies of the Universe) that the Daleks survived this event. (COMIC: Bringer of Darkness)

During the Last Great Time War, the Valeyard turned a temporal superweapon intended for use against the Time Lords against the Daleks, erasing the entirety of their race from the universe, save the Time Strategist who managed to escape into the multiverse. (AUDIO: The War Valeyard) With the Daleks erased, the Time Lords were unable to exactly recall who they had been fighting, leaving them to ponder who their mysterious, unknowable enemy had been. Not even the countless slaves the Daleks had the conscripted to serve as disposable troops could remember whom they had been serving under and so surrendered. (AUDIO: Dreadshade) By manipulating a parallel universe version of Davros, the Time Strategist used dimensional engineering to restore the Dalek Empire to existence, resuming the Time War. (AUDIO: Palindrome, Restoration of the Daleks)

Even as he devised a plan with his future incarnations to save Gallifrey from destruction at the end of the Time War, the War Doctor anticipated that the Daleks would be "destroyed" in the crossfire created by Gallifrey's disappearance. Regenerating the Ninth Doctor lost memory of saving Gallifrey, (TV: The Day of the Doctor) and so believed that both the Daleks and the Time Lords had been wiped out save himself. It thus came to his shock when he encountered the Metaltron, a Dalek survivor of the Time War in Henry van Statten's vault in 2012. The Doctor reasoned that the Dalek must have "fallen through time, the only survivor", and later witnessed its self-destruction after absorbing Rose Tyler's human DNA. (TV: Dalek)

Aboard his ship, Dalek Emperor survived the "inferno" by falling through time to the Fourth Great and Bountiful Human Empire, where he eventually launched an invasion of Earth in 200,100. Recalling the Metaltron's death, Rose reacted with shock when confronted by a single Dalek drone whom she initially mistook for the Metaltron. Identifying the Emperor and his new fleet as the last Daleks in existence, the Doctor made preparations to destroy them with a Delta Wave but ultimately relented from using it, as it would have wiped out all life on Earth as well. The Emperor and his fleet were then destroyed by Rose during her brief transformation into the Bad Wolf. (TV: Bad Wolf/The Parting of the Ways) This event was the end of Dalek history as recorded in The Dalek Conquests, however, its narrator did ponder openly as to whether a species with access to time travel could ever truly go extinct. (AUDIO: The Dalek Conquests)

Confronting the Cult of Skaro, who had escaped the Time War in the Sphere along with the Genesis Ark before emerging in Torchwood London in 2007, the Tenth Doctor insisted that they were the last four Daleks in existence before they opened the Genesis Ark to reveal millions of Daleks whom had been imprisoned by the Time Lords. In the ensuing Battle of Canary Wharf, the Doctor was able to pull the Daleks into the Void, (TV: Doomsday) though the Cult themselves escaped using a temporal shift to Manhattan in 1930, where they were confronted by the Doctor again. The attempted invasion of Manhattan led to the deaths of the Cult bar Dalek Caan, who was acknowledged by the Doctor as the last Dalek in the universe. Refusing to commit genocide by killing him, the Doctor offered Caan his help only for Caan to initiate a temporal shift and escape. (TV: Daleks in Manhattan/Evolution of the Daleks)

In the Planetary Relocation Incident, the Doctor learnt that Dalek Caan had broken the time lock protecting the Time War and retrieved Davros, the Daleks' creator who established a New Dalek Empire in the Medusa Cascade. Affected mentally by his ordeal, Caan was observed to have gone "insane" (TV: The Stolen Earth) but revealed that he had seen the future, maneuvering the Doctor and Donna Noble together to ensure "the end of everything Dalek". Caan entrusted this to the Meta-Crisis Tenth Doctor, who destroyed the Empire by maximising the Dalekanium power feeds aboard the Crucible in an act which the Doctor denounced as genocide. (TV: Journey's End)

Summoned to 1941 by Winston Churchill, the Eleventh Doctor discovered that a single ship with three Daleks had survived. These Daleks had acquired the last remaining Progenitor device. As it would not recognise their "impure" DNA, they goaded the Doctor into providing his testimony verifying them as Daleks and so the Progentior created the first members of the New Dalek Paradigm, whom exterminated their impure predecessors. Recognising that these were the last Daleks, the Doctor attempted to destroy their ship but relented when the Daleks threatened to destroy the Earth, allowing them to use a time corridor to re-establish themselves in the future. (TV: Victory of the Daleks)

Though they succeeded in building a new Dalek Fleet and Dalek Imperial Army, the New Paradigm's ambition for master of space and time was continually thwarted by the Doctor. At the Siege of Trenzalore, the Paradigm learnt that Gallifrey had survived the Time War, and called for reinforcements to ensure that they did not return to the universe. Ultimately, the siege ended when the Time Lords, through a crack in time, bestowed additional regeneration energy to the Doctor, who used it to wipe out the Dalek forces assembled over Trenzalores. Though some observers suggested that this was the end of the Daleks, human historians had reason to believe otherwise; as well as citing the earlier "Final End", they were aware that Skaro survived, hidden behind an invisible shield. (PROSE: Dalek: The Astounding Untold History of the Greatest Enemies of the Universe, TV: The Time of the Doctor)

Alternate timelines

In an alternate timeline where the Cybermen allied with Rassilon to invade the universe across its history, the Fifth Doctor discovered that the Cybermen had inhabited Skaro, having erased the Daleks from history. This timeline was negated when the Twelfth Doctor and Rassilon, who had been betrayed by the Cybermen, regenerated the universe. (COMIC: Supremacy of the Cybermen)