Thirteenth Doctor

The Thirteenth Doctor was the first female incarnation of the Time Lord known as the Doctor and the second incarnation to come from the Doctor's second regeneration cycle.

A day to come
When the Twelfth Doctor broke his toe, Clara Oswald suggested regenerating to heal the injury, but he berated the idea as a waste. (PROSE: The Blood Cell)

While suffering from the common cold, the Twelfth Doctor, overreacting to the illness, considered the possibility of regenerating. (COMIC: The Day at the Doctors)

When the Twelfth Doctor confronted Rassilon on Gallifrey after escaping from his Confession dial, Rassilon contemplated using his gauntlet to force the Doctor to regenerate as a method of torture, but was interrupted before he could. (TV: Hell Bent)

After the Monk invasion, the Twelfth Doctor needed to know if his companion, Bill Potts, was under the control of the Monks, and deceived her into shooting him in a rage to see if she had succumbed to the mind control, secretly putting blanks in all the guns, and faking his regeneration to complete the illusion. He made it look like the process had started, but emerged as himself to show her that he had deceived her. (TV: The Lie of the Land)

Post-regeneration
After the Twelfth Doctor was gravely wounded by the Cybermen on the Mondasian colony ship, the regenerative process began. However, tired of "being someone else", the Doctor delayed the change for some weeks, (TV: The Doctor Falls) until an encounter with his first incarnation, Archibald Hamish Lethbridge-Stewart, and the Testimony caused the Doctor to concede that another regeneration wouldn't "kill anyone". After taking a final look at the universe and providing advice to his next incarnation, the Doctor regenerated inside his TARDIS in an explosive fashion.

Staggering to the console in a daze, the new Doctor examined her face in a reflection, finding her new appearance "brilliant". After she pressed a button on the console, the TARDIS suddenly spiralled into chaos, caused in part by the explosive regeneration. Subsequently, she was thrown out through the TARDIS doors in the confusion after the time rotor exploded, with the TARDIS itself vanishing without the Doctor as she fell towards the Earth. (TV: Twice Upon a Time)

Appearance
This incarnation of the Doctor resembled a woman in her mid-thirties, possessing jaw length blonde hair with dark roots and hazel-coloured eyes. (TV: Twice Upon a Time)

First female Doctor
The Thirteenth Doctor is the first, in the show's history, to be played by a woman. Before Jodie Whittaker, though, the idea of a woman Doctor had been explored.

The idea that a female actor could take the role of the Doctor was first publicly introduced by John Nathan-Turner and Tom Baker in 1980. By Baker's suggestion, he told the press, "I certainly wish my successor luck, whoever he—or she—might be." Peter Davison was cast as the Fifth Doctor, but the idea remained alive.

By the time Whittaker was announced as the actor to follow Peter Capaldi, it was well-established, to viewers and within the Doctor Who universe, that the Doctor could be played by a woman.

Though a parody, The Curse of Fatal Death (1999) by Steven Moffat introduced another Thirteenth Doctor, played by Joanna Lumley. This Doctor, upon regenerating, immediately noted that she had "etheric beam locators". When Emma tells her that those are actual breasts, the Doctor says that she "always wanted to get [her] hands on one of these". At the end, she suddenly finds the Master attractive and walks off with him, arms around each other's waists.

The Big Finish Doctor Who Unbound story Exile (2003), though not set in the prime Doctor Who universe, starred a female Third Doctor, played by Arabella Weir. The story tried to establish that, in this universe, suicide was necessary for a "sex-change regeneration", which was also considered a crime by the Time Lords. Later stories, particularly in the Steven Moffat era, would contradict the idea that changing gender in regeneration was anything out of the ordinary.

In 2010, The End of Time: Part Two had the Eleventh Doctor briefly think he had regenerated into a female form, immediately post-regeneration. He quickly realised that he was mistaken, on finding his Adam's apple.

In 2011, Neil Gaiman's The Doctor's Wife was the first to make direct reference to a Time Lord changing gender through regeneration. The Doctor talks of the Corsair, a "fantastic bloke", who was also a "bad girl" in a couple of their incarnations.

In 2013, The Night of the Doctor had the Sisterhood of Karn offer the Eighth Doctor the choice of "man or woman", for his approaching regeneration.

In 2014, Steven Moffat introduced audiences to, revealed in Dark Water to be the first female incarnation of the Master. Missy was a recurring character in Series 8, 9, and 10.

In 2015, Hell Bent showed audiences the regeneration of the General from a male body to a woman, the first time such an instance occurred on-screen, though the Big Finish audio story, The Black Hole, had a male to female regeneration eighteen days before the episode aired. A year later, Enemy Lines showed the first female to male regeneration.

In 2017, World Enough and Time included a rooftop conversation, between the Twelfth Doctor and Bill, in which he's only "fairly sure" that his first incarnation was a man, as it was a long time ago. The Twelfth Doctor here claims that Time Lords are "beyond [the] petty human obsession with gender and its associated stereotypes".

The same year, the audio story The Conscript included a conversation between the Eighth Doctor and a Time Lord soldier, where the Doctor stated that he was a "he, for now at least."

Other matters
This is the only known incarnation of the Doctor that is not known to have participated in the Last Great Time War.

She is also the first incarnation that is completely unknown to River Song; the last time she met the Doctor before her death, she encountered the Twelfth Doctor, the first in a new regeneration cycle, and had not been aware that he had any incarnations past the Eleventh. She is also the first incarnation who is not known to have encountered Clara Oswald or any of her various splinters.