The Doctor's species

Much like their age and the true circumstances of 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)

Time Lord
The Doctor usually identified themselves as a Time Lord (TV: The War Games, Pyramids of Mars, The Night of the Doctor,etc.) from the planet Gallifrey in the constellation of Kasterborous. (TV: The Day of the Doctor)

A previous life, a previous race
According to one account, however, the Doctor's childhood on Gallifrey with the Master was a result of their having been regressed into a child, and their memories redacted, after 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 DNA, Tecteun was still no closer to discovering the true origins of the Doctor. (TV: The Timeless Children)

In a similar but distinct 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, the Other was was "neither an angel nor a djinn". (PROSE: Head of State, Interference)

Half-human?
The Eighth Doctor had vivid memories of his childhood with his father on Gallifrey, but also claimed to be half-human on his mother's side. 's analysis of the Doctor's retinal structure seemingly confirmed this, (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)

Human
In other accounts, the First Doctor and the Second Doctor were identified as human beings (PROSE: Doctor Who and the Daleks) whose regeneration powers were a function of the TARDIS they piloted. (TV: The Power of the Daleks) The Daleks believed that it was as a result of his many travels through Time that the Doctor had become "more than human". (TV: The Evil of the Daleks)