The Doctor's species

Much like their age and their early life, the Doctor's species was a matter of much contention due in part to shifting timelines. (PROSE: Celestial Intervention - A Gallifreyan Noir)

The vast majority of sources agreed that the Doctor was a Gallifreyan and a Time Lord, (TV: The War Games, et al.) but a few suggested that they had different origins. Various accounts identified the Doctor as being fully or partially human, (PROSE: Doctor Who and the Daleks, TV: Doctor Who, et al.) having once been the Timeless Child from an unknown species, (TV: The Timeless Children) or as the product of still stranger origins. (PROSE: The Death of Art, Sometime Never..., et al.)

Shifting of timelines
According to one young member of Faction Paradox, the Doctor was originally a human from a planetary colony of the 49th century, but fled when the Enemy invaded their home. Subsequently, the Enemy kept rewriting the Doctor's history, eventually resulting in the version of their past that they remembered as the Eighth Doctor, where they had been born a Time Lord, albeit possibly with some human ancestry. (PROSE: Unnatural History) Indeed, in their earliest remembered lives, such as the First Doctor, the Doctor sometimes referred to themself as human. (TV: The Sensorites) While there was no way to prove the boy's claims, the Eighth Doctor found these possible revelations disturbing. (PROSE: Unnatural History) A little while later, after discussing the Buddhist parable of the man who dreamt he was a butterfly, the Eighth Doctor told Sam Jones that he was "just a Time Lord dreaming he’s a man", before frowning and adding: "Or is it the other way around?". (PROSE: Interference - Book One)

When researching the Doctor after the First Doctor fled Gallifrey, former CIA agent Maris found many, contradictory, documents concerning the Doctor's early life; one birth notice claimed he was the son of a human mother and a Time Lord father, while another claimed he was a high-born Time Lord of the House Lungbarrow created through a Loom. Maris then found three other birth documents that also disagreed on the Doctor's origin. Maris came to learn the Doctor's past was constantly shifting due to their travels through time. (PROSE: Celestial Intervention - A Gallifreyan Noir)

A Gallifreyan Time Lord?
Although human-like in appearance and broad mannerisms, the Doctor was by most accounts not human; (PROSE: Who is Dr Who?) the Doctor usually identified themselves as a Time Lord (TV: The War Games, Pyramids of Mars, The Night of the Doctor, et al.) from the planet Gallifrey in the constellation of Kasterborous. (TV: The Day of the Doctor) The Fourth Doctor once explicitly referred to himself as "a native Gallifreyan Time Lord". (PROSE: A Letter from the Doctor)

Explaining that the Time Destructor would not affect him as gravely as a human, the First Doctor told Steven Taylor that he was not of "[Steven's] race", being "already" over 700 years old. (PROSE: The Mutation of Time)

The Dalek Survival Guide stated that the Doctor was only "possibly" a Time Lord. (PROSE: Dalek Survival Guide)

The DoctorDonna said that the Tenth Doctor was "just" a Time Lord. She declared that not having even "a little bit of human" held him back. (TV: Journey's End)

A previous life, a previous race
According to one account, the First Doctor was indeed the first incarnation of the Doctor as such, but was the reincarnation of the Other, one of the Founders of Gallifrey, whose mind and genetic structure had been redistributed into the Loom which created the Doctor many millennia later. (PROSE: Lungbarrow) According to The Thousand and Second Night, a highly figurative account of early Gallifreyan history, an individual who was "neither an angel nor a djinn" was involved in the Eternal War. The Shift claimed to be them. (PROSE: Head of State)

In a similar but distinct account, however, the Doctor's childhood on Gallifrey with the Master was a result of their having been regressed into a child, after having had their memories redacted, following a large number of regenerations; they were originally the Timeless Child, a being of an unknown species whom the Shobogan explorer Tecteun adopted and brought back to Gallifrey, harnessing the Child's regenerative abilities to turn her people into the Time Lords. Though she sequenced her adopted child's entire genome, Tecteun was still no closer to discovering the true origins of the Doctor.

The account that stated the Timeless Child's biodata was what gave the Time Lords the power to regenerate (TV: The Timeless Children) aligned with Richard Francis Burton's theory that they only had the ability because they modified their genetic makeup with the Yssgaroth's "taint". (PROSE: The Book of the War) The vampyres were indeed searching for a Child-That-Was-Taken. (PROSE: Out of the Box)

Half-human?
The Eighth Doctor had vivid memories of his childhood on Gallifrey, but he also claimed that his mother was human; 's analysis of the Doctor's retinal structure seemingly confirmed that he was half-human, (TV: Doctor Who) although the Eighth Doctor would later claim that he had tricked "his greatest enemy" into thinking him to be half-human using a "half-broken Chameleon Arch". (COMIC: The Forgotten) While the Eighth Doctor was on Dreamstone Moon, Isabella Cleomides reported that his retinal structure instead denoted Partriscisnad origins. (PROSE: Dreamstone Moon)

The Eighth Doctor, when being interrogated about his origins, also once claimed that he was from Andromeda, his mother having been "abducted by little green men". (PROSE: Seeing I)

Me briefly speculated that the prophecy of the Hybrid referred to the Doctor, believing him to possibly be half-human based on his tendency to spend time on Earth. However, the Twelfth Doctor laughed at this theory. (TV: Hell Bent)

While the Relic, the corpse of the Doctor's final incarnation, was in storage awaiting auction in the Unthinkable City, Qixotl saw Sam Jones and Kathleen Bregman on the security feed attempting to reach it. Qixotl speculated that the Relic's lingering consciousness had telepathically summoned them, as "the Doctor had a thing about humans, according to the old stories; something to do with his retroactive ancestry, apparently". (PROSE: Alien Bodies)

Human
By other accounts, the First Doctor and the Second Doctor were human beings (TV: The Evil of the Daleks, PROSE: Doctor Who and the Daleks, The Monsters from Earth) whose powers of renewal were a function of the TARDIS they piloted. (TV: The Power of the Daleks) The Daleks once believed that it was as a result of his many travels through time that the Doctor had become "more than human", and the Second Doctor himself suggested to the Daleks that he might otherwise be a potential source from whom the Human factor could be sampled, although he also told Jamie that he came from another planet. (TV: The Evil of the Daleks)

When pleading with Edal, the First Doctor referred to himself as a human being, speaking of "human beings, like you and me". (TV: The Savages) He also referred to both himself and Susan Foreman as humans, remarking to Captain Maitland that "[cats] can see better than we humans, because the iris of their eyes dilates at night". (TV: The Sensorites)

One account referred to the Doctor as the greatest human mathematician, whose equations had at long last united space and time fully into the inextricable concept of the Idea of the Living Matter. This had allowed him to construct the TARDIS, a machine which could withstand and travel through Eternity and Infinity in a microsecond. (PROSE: The Equations of Dr Who)

The Third Doctor once visited a parallel universe where he encountered a version of himself who lived on Earth. This Doctor did not recognise the TARDIS nor did he have any knowledge of extraterrestrials or space travel. (COMIC: Who's Who?)

While in a human persona named John Smith, the Seventh Doctor wrote a children's story called The Old Man and the Police Box, about a human scientist from Victorian England who invented a time-travelling police box, established civilisation on the primitive planet Gallifrey, then fled back to Earth after the Gallifreyans become staid and obsessed with law. (PROSE: Human Nature)

Other possibilities
According to one account, Dr. Who was from Earth, along with Ben and Polly; he outright identified himself and his companion originating from the planet. (PROSE: The Dream Masters)

In the post-War universe where the Time Lords never existed, (PROSE: The Adventuress of Henrietta Street) the Doctor was originally a member of the Council of Eight named Soul, who lost his memory following a confrontation with the Eighth Doctor. (PROSE: Sometime Never...)

When the vampire Joanna Harris, having difficulty believing in Time Lords, asked the Eighth Doctor why he hadn't simply introduced himself as "Osiris, or the archangel Gabriel", the Doctor replied with dismay, "You guessed." He then grinned and winked, and James Court, who witnessed the interaction, decided to count this as a joke. (PROSE: Vampire Science) Osiris was king of the Osirians prior to his murder by Sutekh. (AUDIO: Coming to Dust, PROSE: The Sands of Time, et al.)

The Doctor occasionally appeared to his companions as something godlike or monstrous. Bernice Summerfield saw the Seventh Doctor as a transdimensional monster "crammed down into a parody of human flesh". (PROSE: Transit) Mavic Chen believed that the First Doctor's resemblance to "an Earth creature" was merely "a disguise". (TV: The Daleks' Master Plan)

Roz Forrester suggested that he matched the description of Nyarlathotep, (PROSE: The Death of Art) the darkest and greatest of the Old Ones. (PROSE: The Quantum Archangel) When the Eighth Doctor displayed knowledge of the name the Great Old Ones gave to the "Fire of the Last Birth" at the beginning of the universe, Compassion suggested that he might be "a Great Old One on [his] mother’s side". (PROSE: The Taking of Planet 5)

Following their first encounter with a Slitheen, Jackie Tyler wondered to Mickey Smith if the Ninth Doctor had a "great big green thing" inside him as well, to which Mickey said he "wouldn't put it past him". (TV: World War Three) Following his regeneration, the Tenth Doctor flatly assured Rose Tyler that he was not a Slitheen when she suspected him of being so. (TV: Born Again)

Upon learning from the Tenth Doctor that he was an alien, Donna Noble assumed that he was a Martian and repeatedly referred to him as such during the Racnoss invasion of Earth, though he repeatedly insisted that he was not from Mars. Lance Bennett overheard Donna's use of the term "Martian" and identified him to the Empress of the Racnoss. It was only when the Racnoss, an old enemy of the Time Lords, repeated the misconception that the Doctor disclosed his home planet as being Gallifrey. (TV: The Runaway Bride) Later, when she started travelling with the Doctor, Donna Noble began to wonder exactly what kind of alien he was, which led her to wonder if he was like the aliens featured in the "old TV show" V; that he had rubber skin, and that he'd pull it off to reveal a big "lizard face" when he was relaxing. (PROSE: The Fires of Pompeii)

Amy Pond asked the Eleventh Doctor if he was a "space squid" or a "tiny little slug in a human suit", suggesting the latter to explain what she found as his peculiar way of walking. The Doctor insisted to Amy that his external appearance was his true form. (TV: Meanwhile in the TARDIS)

Later developments
The Fugitive Doctor used a Chameleon Arch in order to transform herself into a human, named Ruth Clayton, in order to evade the Division. She later had her identity restored, along with her biodata. (TV: Fugitive of the Judoon)

The Second Doctor was infused with Androgum genetic material by Dastari, making him 50% Androgum. He began to mutate as it became the dominant factor. He was soon 80% Androgum, and the Sixth Doctor stated that by the time the effect reached him, it would be close to a hundred percent, and that he was already beginning to feel changes. Dastari did not get a chance to stabilise the Second Doctor's cell structure, so his body eventually rejected the transfusion. (TV: The Two Doctors)

The Third Doctor was briefly mutated into a Primord through physical contact with Liz Shaw, who had been exposed to Stahlman's ooze. (AUDIO: Primord)

The Fifth Doctor allowed himself to become a vampire so he could stop Ruath's plan to resurrect Yarven. Following this, he changed himself back to normal. (PROSE: Goth Opera)

The Seventh Doctor, pursued by a family of Aubertides, purchased a device to biologically transform himself into a human named John Smith, complete with a life's worth of false memories. (PROSE: Human Nature) Later, the Tenth Doctor, pursued by the Family of Blood, used a Chameleon Arch to change himself into a human, again named John Smith. (TV: Human Nature) This same sequence of events happened many times, in many ways, to different incarnations of the Doctor. (WC: Shadow of a Doubt)

Other realities
Tardis Tails, the Eighth Doctor's counterpart in a parallel world, was an anthropomorphic cat. Another alternative Eighth Doctor was a cyborg. (COMIC: The Glorious Dead)

In one of the infinite parallel universes of "possible space", (COMIC: Fire and Brimstone) the Doctor was the half-human, half-Time Lord son of Ulysses and Annalisse. (PROSE: The Chronicles of Doctor Who?)

Though an alternate Ninth Doctor identified himself as a Time Lord and "not human", the Master observed that he was prone to a number of "infuriatingly human trait[s]". (WC: Scream of the Shalka)

Behind the scenes

 * According to Donald Tosh, (BBC DVD: The Time Meddler) the commissioning script editor and (uncredited) co-author of The Celestial Toymaker, the intention was that the Toymaker was, like the Monk who had predated him, a member of the Doctor's own race.
 * In an early draft of The End of Time, Russell T Davies had the Tenth Doctor address the "half-human" statement the Eighth Doctor made in the 1996 TV movie, dismissing it as "a forty-eight-hour bug". The line was cut by Davies for several stated reasons, including the fact it would have confused viewers who were only familiar with the events of TV: Human Nature. (REF: The Writer's Tale - The Final Chapter)