Venusian aikido

Venusian aikido (sometimes called Venusian karate) was an unarmed combat style used by the Doctor in multiple incarnations, including their third, fourth, fifth, sixth, eighth, twelfth, and thirteenth, as well as several of their companions including Sarah Jane Smith, Jo Jones, and River Song, to defend themselves and others.

Nature
According to some accounts, and the Thirteenth Doctor, it was developed by Venusian nuns (TV: The Ghost Monument) on Venus, which meant it worked best with five arms and five legs (PROSE: First Frontier), with the Doctor musing that he was one of the few two-armed beings to become truly adept with the martial art; (PROSE: The Eight Doctors) when asked by Nardole how he managed Venusian aikido, as, to Nardole's knowledge, one "needed four arms for Venusian", the Doctor quipped that he had "hidden talents — as well as hidden arms". (TV: World Enough and Time) Another account stated that the Doctor himself had invented it. (PROSE: Interference - Book One)

It could be used to immobilise an opponent by using pressure points (TV: The Mind of Evil, Inferno) and perform joint locks, throws and kicks. (TV: The Claws of Axos) It tended to use the attacker's own movements against them. (PROSE: Freedom) These were effective against many different humanoid species, but were useless against non-human duplicates and seemed to have no effect on Ogrons or Sontarans. (TV: The Claws of Axos, Day of the Daleks, The Time Warrior) While amnesiac and trying to remember his Venusian aikido training, the Eighth Doctor recalled "flying through the air" before turning back to face his Venusian instructor. (PROSE: The Eight Doctors)

The Doctor
The Second Doctor learned the arts of Venusian Aikido whilst on Venus with Jamie McCrimmon and Victoria Waterfield. (AUDIO: Voyage to Venus) The Eighth Doctor would remember being taught by "a many-armed glowing-eyed being in a misty cavern". (PROSE: Endgame)

The Third Doctor used it to disable Professor Stahlman. He claimed that, if the move was held for a period, it would paralyse the target permanently. (TV: Inferno)

The Third Doctor tried to use Venusian Aikido against Primords. When this didn't work he moved on to Martian karate, but this had no effect either. (PROSE: Inferno)

The Third Doctor was also forced to use Venusian Aikido against several Sea Devils. (TV: The Sea Devils)

The Third Doctor used his knowledge of Venusian martial arts to defend himself against attacking Uxarieans. (TV: Colony in Space)

The Third Doctor used Venusian Aikido to subdue Varan when he was attacked whilst trying to escape the Skybase (TV: The Mutants)

The Third Doctor also proved himself a formidable opponent using Venusian martial arts against several guards. (TV: The Green Death)

The Third Doctor also tried to use Venusian Aikido against Jingo Linx, but it proved to be ineffective. (TV: The Time Warrior)

The Third Doctor again employed Venusian Aikido when he was forced to fight several Exxilons on the planet Exxilon when they tried to capture him. (TV: Death to the Daleks) The Third Doctor used Venusian Aikido against Remoraxians. (COMIC: In With the Tide)

The Third Doctor used Venusian Aikido to disable the hypnotised Ned. (COMIC: The Celluloid Midas)

The Fifth Doctor used Venusian Karate against Adric. (PROSE: First Born)

In an attempt to trick Curatrix Zennox and stop her from completing her plan to bring back the Cybermen, the Sixth Doctor claimed that he used Venusian Karate to overpower Jamie McCrimmon. She thought he was making that up. (AUDIO: Last of the Cybermen)

The Eighth Doctor, despite his amnesia, remembered a Venusian Aikido lesson and used it against Mo. (PROSE: The Eight Doctors)

The Eighth Doctor used Venusian Aikido against Grandfather Paradox, who countered his every move. Grandfather then boasted he was the only one-armed being who ever mastered it. (PROSE: The Gallifrey Chronicles)

The Eighth Doctor used Venusian Aikido against C'rizz to stop him from strangling Charley, although the Doctor later admitted that he was out of practice. (AUDIO: Faith Stealer)

The Eighth Doctor used Venusian Aikido to defend himself against Destrii. (COMIC: Ophidius)

The Twelfth Doctor used Venusian aikido on Abesse after she repeatedly attacked him in the Prison canteen. He stated that he didn't use it on ladies as a general rule, but that Abesse wasn't a lady. (PROSE: The Blood Cell)

The Twelfth Doctor used Venusian aikido on Robin Hood to knock his sword from his grip. (TV: Robot of Sherwood)

The Twelfth Doctor used Venusian aikido on Jorj, successfully flipping him to the ground, knocking him out. (TV: World Enough and Time)

The Twelfth Doctor used Venusian aikido to disarm a student who was threatening him with a gun. (COMIC: The Hyperion Empire)

Calling herself a "grandmaster pacifist", the Thirteenth Doctor used Venusian aikido to stun Epzo with only one finger. The Doctor commented that the Venusian nuns who created it were "clever." (TV: The Ghost Monument) When Jarva Slade pointed a gun at her, she also used the same move to disable him briefly, to disarm the man, who recovered once she moved her finger away. (TV: Kerblam!) The Doctor used Venusian aikido again in Hong Kong in 1972, fighting against Chen Luo’s men alongside Bruce Lee who was intrigued by her fighting style. (COMIC: The White Dragon)

Others
In their time together, the Third Doctor taught Jo Grant Venusian aikido. Forty years later in her personal timeline, she used it against him to knock the Doctor unconscious, intent on sacrificing herself in the Doctor's place. (AUDIO: The Sacrifice of Jo Grant)

Sarah Jane Smith knew Venusian aikido. (TV: A Girl's Best Friend)

River Song learned Venusian martial arts from the Venusian Martial Arts Academy on one of her honeymoons because she misread the brochure. (AUDIO: The Sonomancer)

The Thirteenth Doctor taught Venusian aikido to Bruce Lee in 1972. He planned to use what he had learnt in his movie, Enter the Dragon. (COMIC: The White Dragon)

After learning of the fighting style in a fight with Rey Malvado, Señor 105 studied Venusian martial arts at the House of Five Creeds with Theo Possible, Litany Chromehurst, and the adventurer Possible called "El Jefe". (PROSE: The Rise & Fall of Señor 105)

Behind the scenes

 * Barry Letts was opposed to the idea of an aggressive Doctor. Therefore, Terrance Dicks suggested aikido as it has no attacking moves. (DOC: Can You Hear the Earth Scream?)
 * In the comic story Terrorformer, which is set after Robot of Sherwood, the Twelfth Doctor states that he has just remembered knowing Venusian karate, suggesting that Venusian karate and Venusian aikido may be different disciplines.