The Doctor's family

The Doctor's familial relations were numerous and paradoxical. (PROSE: Celestial Intervention - A Gallifreyan Noir) According to the Seventh Doctor, they would rather forget about him. (AUDIO: Master) The Doctor's brother, Irving Braxiatel, once stated the urge to leave the Time Lord homeworld of Gallifrey "[ran] in the family", as he, (AUDIO: Beyond) the Doctor, (TV: An Unearthly Child) their father Ulysses, (PROSE: Unnatural History) and Susan Foreman were all known to have done so. (TV: An Unearthly Child)

Official Celestial Intervention Agency briefings claimed that all of the Doctor's close family except for his granddaughter Susan had perished during the Prydonian Academy Revolution, the event which prompted the Doctor and Susan to run away from Gallifrey. (PROSE: CIA File Extracts)

Sarah Jane Smith once referred to the Doctor's companions as their family, telling the Tenth Doctor, "You act like such a lonely man, but you've got the biggest family on Earth!" (TV: Journey's End) The Doctor chose to think of the universe as their foster family, after their parents "decided to opt out of their responsibilities." (PROSE: Beltempest)

Ancestors
According to one account, the Doctor was one of the forty-five cousins created by the Loom of the House of Lungbarrow on Gallifrey. (PROSE: Lungbarrow, Celestial Intervention - A Gallifreyan Noir) At other times, the Doctor stated that he had parents, including a Time Lord father (TV: Doctor Who, PROSE: The Infinity Doctors, Unnatural History, Matrix) and a human mother. (TV: Doctor Who, PROSE: Alien Bodies, The Infinity Doctors, Grimm Reality, Unnatural History, The Shadows of Avalon, Celestial Intervention - A Gallifreyan Noir) Some accounts held that the Doctor's mother was the human Penelope Gate. (PROSE: The Infinity Doctors, The Gallifrey Chronicles)

In a third account of the Doctor's origins, they were originally the mysterious Timeless Child, discovered and adopted by the Shobogan traveller Tecteun, who brought her child back with her to Gallifrey. (TV: The Timeless Children)

Patience taught the Doctor's grandfather, (PROSE: Cold Fusion) and the Thirteenth Doctor spoke of several grandmothers. (TV: It Takes You Away)

The Eleventh Doctor spoke of his godmother, (TV: Vincent and the Doctor) and his great-aunt Inertia. (GAME: The Mazes of Time)

The Eighth Doctor remembered coming from an "important", political family on Gallifrey, and growing up with all the privilege that entailed. (AUDIO: Must-See TV)

Siblings
The Doctor had at least one brother, Irving Braxiatel, (PROSE: Tears of the Oracle, AUDIO: Disassembled, PROSE: ...Be Forgot, Big Bang Generation, Celestial Intervention - A Gallifreyan Noir, TV: Smith and Jones) who became an associate of the Doctor's companion Bernice Summerfield. (PROSE: Tears of the Oracle) Braxiatel was a Cardinal of Gallifrey, (AUDIO: Weapon of Choice) and later became High Chancellor, though in exile. (AUDIO: Pandora) He was also the owner of the Braxiatel Collection, (PROSE: Tears of the Oracle) which the Doctor and Romana once compared to the Louvre in Paris. (TV: City of Death) The Doctor had one niece by Irving Braxiatel, Maggie Matsumoto. (AUDIO: The Empire State)

The Thirteenth Doctor recalled once having had sisters, (TV: Arachnids in the UK) though another account indicated the Doctor never had an older sister. (PROSE: Dragonfire) Irving Braxiatel hinted that he had once lost a sister, or a daughter. (PROSE: Tears of the Oracle)

At the Eighth Doctor and Scarlette's wedding in the post-War universe, the Man with the Rosette sat at the table reserved for the Doctor's family. (PROSE: The Adventuress of Henrietta Street)

Descendants
The Doctor had, in the Tenth Doctor's own words, been "a dad" (TV: Fear Her) and "a father". (TV: The Doctor's Daughter) These children were "sons or daughters, or both." (PROSE: The Eleventh Tiger) The Twelfth Doctor claimed he had "dad skills". (TV: Listen) Clara Oswald also claimed the Doctor had once had "children". (TV: Death in Heaven)

Susan's father was a Cardinal on Gallifrey, and had a wife who died giving birth to Susan. (PROSE: Cold Fusion, Lungbarrow) It was unclear which of them was the descendant of the Doctor, or if either was. However, in another universe, the Doctor's daughter was Susan's mother. (AUDIO: Auld Mortality)

The Doctor also had several grandchildren, (TV: Death in Heaven) including Susan, (TV: An Unearthly Child, et al.) John, and Gillian Who. (COMIC: The Klepton Parasites, PROSE: Beware the Trods!, et al.) Some accounts referred to Susan as "the Other's" granddaughter. (PROSE: Lungbarrow)

At one point, the Doctor became the adoptive father to a female Time Lord named Miranda Dawkins, whom the Eighth Doctor reared until her mid-teens. (PROSE: Father Time) Miranda later gave birth to a daughter, Zezanne, and died while trying to protect the Doctor. (PROSE: Sometime Never...)

The Doctor also had a great-grandson named Alex, the son of Susan and David Campbell. (AUDIO: An Earthly Child) Alex went on several adventures with the Eighth Doctor and backpacked around the Earth with Lucie Miller before they were both killed by the Daleks. (AUDIO: Lucie Miller, To the Death) Susan and David also had adopted children, Barbara, Ian and David Junior. (PROSE: Legacy of the Daleks)

Genetic material from the Doctor in their tenth incarnation was used to create a daughter, Jenny, via progenation. The Doctor explained to Donna Noble and Martha Jones that due to the way his DNA was processed, he was Jenny's "biological mother and father". Although initially spurning her, he soon considered Jenny his daughter and invited her to travel with him in the TARDIS. Before she could join him, however, she was shot by General Cobb. The Doctor believed Jenny to have died, and departed. (TV: The Doctor's Daughter) Unbeknownst to him, she survived and set out on her own life of adventure, (TV: The Doctor's Daughter, AUDIO: Stolen Goods, et al.) even sharing one adventure with an earlier incarnation, the Fifth Doctor. (AUDIO: Relative Time)

When the Earth was relocated to the Medusa Cascade, an instantaneous biological meta-crisis was created; this Meta-Crisis Tenth Doctor was later was exiled by the Tenth Doctor proper to a parallel universe. (TV: Journey's End) In this parallel universe, the Meta-Crisis Doctor, having since taken on the name "Corin", entered into a relationship with Rose Tyler. The two had a child together. (PROSE: The Turning of the Tide)

Fate
Much of the Doctor's family died or went missing. The majority of the Doctor's Cousins from House Lungbarrow died during the 673 years they spent trapped under Mount Lung after the House buried itself in shame over the murder of it's Kithriarch, Ordinal General Quences- including Housekeeper Satthralope who was crushed by her own chair, Cousin Arkhew who was strangled by Cousin Owis, Cousin Luton who got stuck in a chimney, and Cousin Glospin who was killed by Badger to protect the Seventh Doctor. On the eve of Susan's Birth, in some prior lifetime to what is generally accepted as his First Incarnation, the Doctor's First-Born son faced down a squad of Chancellery Guard sent to purge the Doctor and Patience's children living at House Blyledge, presumably only the Doctor, Patience and Susan survived the culling, rescued by a figure from Patience's relative future, The First Doctor. The Other later told Susan that her mother died during the birth and that her father was later sent to serve in the Vampire Wars whereupon he perished aboard a Bowship. (TV: The Tomb of the Cybermen, The Curse of Fenric, PROSE: Lungbarrow, AUDIO: To the Death, AUDIO: Cold Fusion, TV: The Woman Who Fell to Earth) After the last day of the Time War, the Tenth Doctor, while telling Donna that he'd been a father before, explained that he "lost all that a long time ago along with everything else." (TV: The Doctor's Daughter) The Eleventh Doctor involuntarily reacted to Corc's accusation that he had never lost a child. (PROSE: Dark Horizons) Even after the Doctor realised that Gallifrey and the Time Lords were not destroyed at the end of the Time War, the Doctor still believed their family, including the missing children and grandchildren, to be dead. (TV: Death in Heaven, The Woman Who Fell to Earth)

Affairs
The Tenth Doctor told Sally Sparrow that he was "rubbish at weddings, especially [his] own". (TV: Blink)

The First Doctor was accidentally engaged to Cameca in the 15th century when he drank cocoa with her. (TV: The Aztecs)

An earlier incarnation had been wed (PROSE: Cold Fusion) to Patience and they were said to have had a number of children and grandchildren. (PROSE: The Infinity Doctors)

After Gallifrey was destroyed in the War in Heaven, the Eighth Doctor married Scarlette in order to ceremonially tie himself to the planet Earth. (PROSE: The Adventuress of Henrietta Street)

The Tenth Doctor romanced and later married Elizabeth I. (TV: The End of Time, The Day of the Doctor, PROSE: Suspicious Minds) She later declared him an enemy after he failed to return as promised. (TV: The Shakespeare Code) The Tenth Doctor implied he had been married several times prior to Queen Elizabeth, as he remarked to Sally Sparrow about being "rubbish at weddings, especially [his] own". (TV: Blink) In his eleventh incarnation, the Doctor accidentally became engaged to Marilyn Monroe, and married her the same night in what he later claimed was not a real chapel. (TV: A Christmas Carol)

River Song often hinted that she and the Doctor had a physical relationship somewhere in her past and his future relative to the Eleventh Doctor's encounter with the Silence in Florida. (TV: Silence in the Library / Forest of the Dead, The Time of Angels / Flesh and Stone, The Pandorica Opens / The Big Bang, Day of the Moon) The Eleventh Doctor, operating a Teselecta shaped like himself, performed a "quick version" of a wedding ceremony with River because they were in the middle of a combat zone in an alternate reality. They repeatedly referred to each other as husband and wife after the ceremony. (WC: Asylum of the Daleks Prequel, TV: The Wedding of River Song, The Angels Take Manhattan, The Name of the Doctor, The Time of the Doctor, The Husbands of River Song, AUDIO: The Boundless Sea, Five Twenty-Nine, The Eye of the Storm, PROSE: Suspicious Minds)

According to Clara Oswald, by the time of the Doctor's twelfth incarnation, he had been "married four times, all deceased". (TV: Death in Heaven)

Myths
Martha Jones had believed that the Master was the Doctor's "secret brother [or something]", to which the Tenth Doctor told her that she had "been watching too much TV." (TV: The Sound of Drums)

Behind the scenes

 * Martha's belief that the Master was the Doctor's "secret brother" was first floated as a revelation about the character back in the Jon Pertwee-era. The idea was reignited years later in the Peter Davison-era story Planet of Fire, with Anthony Ainley's version of the Master, before seemingly burning up, exclaiming "Won't you show mercy to your own…", never finishing the sentence. According to the DVD commentary, Fiona Cumming asked John Nathan-Turner how the line was to end, to which he replied, "brother". It was also used in several pitches for the Eighth Doctor TV projects which eventually ended up as the 1996 Doctor Who TV movie; there, the Master would have been Ulysses' son by his legitimate Gallifreyan spouse, while the Doctor was Ulysses' son with a human woman, making him and the Master half-brothers.
 * David A. McIntee once pitched a Fifth Doctor novel which would instead have revealed the Doctor and the Master as former spouses, in a plotline allegedly inspired by War of the Roses. The pitch was refused with a "death-stare" from Gary Russell.