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.

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.

Her hands were noticeably smaller than those of her predecessor, resulting in the ring she had worn in her previous incarnation falling onto the floor upon regeneration. She was shorter in stature than her previous incarnation as well; the Twelfth Doctor's coat appeared at least one size too big for her. (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.

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. The story also depicted this first woman Doctor as a failure, hiding from the Time Lords: an alcoholic with a boring job at Sainsbury's, and a dull life, void of adventure.

Later stories, particularly in the Steven Moffat era, would contradict the idea that changing gender in regeneration was anything out of the ordinary, and certainly lifted the veil of shame.

Build-up in Doctor Who
By the time Jodie 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.

The Fifth Doctor stated that one never quite knew what they were going to get. (TV: Castrovalva) The Ninth Doctor stated before regeneration that it was a dodgy process and one never knew what they'd end up with. (TV: The Parting of the Ways) According to the Seventh and Tenth Doctors, regeneration was a lottery. (TV: Time and the Rani, The Day of the Doctor)

In the 2002 audio Seasons of Fear, the Eighth Doctor informed his future enemy Sebastian Grayle that he wasn't "a glamorous woman at the moment", hinting at his ability to become such a thing in the future.

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.

Neil Gaiman's script for The Doctor's Wife (2011) was perhaps the first to make 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.

Just the following season, Steven Moffat's Dark Water introduced audiences to, the first female incarnation of the Master. Series 9's 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.

Series 10's 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".

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.

Like the Twelfth Doctor in The Day of the Doctor before her, this incarnation is first glimpsed with a close-up shot of her eyes in Twice Upon a Time, coincidentally both of these are multi-Doctor stories.