20th century
On Earth, the 20th century was one of the most turbulent, violent, yet progressive centuries in the planet's history. In addition to major conflicts including the First (TV: To the Last Man) and Second World Wars (TV: The Empty Child / The Doctor Dances), humankind began to explore beyond their homeworld for the first time, and also began to make huge leaps in technological advancement. (TV: Day of the Moon) It was also during the 20th century that many world governments learned of the existence of extraterrestrial lifeforms (TV: Spearhead from Space), although the general public would remain in the dark about this until the beginning of the 21st century. (TV: Aliens of London) The Torchwood Institute, founded in the 19th century, began to gain power and influence in this century (TV: Fragments), while several attempted alien invasions resulted in the formation of the United Nations Intelligence Taskforce. (TV: The Web of Fear, The Invasion)
The Doctor had a great affinity for this century, though his first incarnation initially claimed to tolerate but not enjoy it. (TV: An Unearthly Child) He lived during this time period for several years as an exile from Gallifrey (during his third incarnation) (TV: Spearhead from Space, Doctor Who and the Silurians, et al.) and again for a number of months in 1913 and 1969 in his tenth incarnation (to name just two examples). (TV: Human Nature / The Family of Blood, Blink) Many of the Doctor's known Earth companions came from this century, as he visited it often. (TV: An Unearthly Child, The Massacre of St Bartholomew's Eve, The War Machines, Spearhead from Space, Terror of the Autons, The Time Warrior, et al.)
As with most centuries of the first two millennia, the 20th century was home to Jack Harkness, Amy Pond and an Auton duplicate of Rory Williams. A version of Jack from around the time of the deaths of Toshiko Sato and Owen Harper existed in this century, having been buried alive in the 1st century by his brother, Gray. He perpetually died and resurrected an unknown number of times in an earthen tomb underneath Cardiff. (TV: Exit Wounds) Meanwhile, a near-dead Amy Pond was kept alive inside the Pandorica, beginning in the 2nd century. An Auton version of Rory kept vigil near her the entire time. They both awaited a moment in the mid-1990s when a young Amelia Pond would touch the outside of the Pandorica and restore Amy to full health. (TV: The Big Bang)
It was substantially unclear whether the events of the subsequent Big Bang Two erased Amy and Rory's presence in the 20th century. This ambiguity was caused, in part, because the non-Auton, married Rory Williams claimed to have remembered being "made of plastic" at his wedding reception, suggesting that, at least inasmuch as he was concerned, he and Amy were present in the 20th century. (TV: The Big Bang) Amy seemed to also remember those events, and displayed a fondness for the Auton Rory both during her honeymoon (TV: A Christmas Carol) and during a kind of lullaby to her newborn child Melody Pond. (TV: A Good Man Goes to War)