Torture was the deliberate inflicting of pain, usually as a punishment against criminals or an aid in interrogations.
The Third Doctor was tortured by Luigi Rossini in an attempt to find out why he was asking about Professor George Philips. (TV: Terror of the Autons)
Jane Page was experienced in torture and thought it was a matter of technique. She explained that "eyes are good. Nails and teeth if you have the equipment. Breasts, if it's a woman." Her tip was to start with psychological torture as it got the victim in a better state. (PROSE: Falls the Shadow)
Jack Harkness related to a captive named Martin that he had experience in torturing prisoners, and that, "a long time ago", he had "quite a reputation as the go-to guy" in the event of needing to force information out of a person and knew just "where to apply the tiniest amount of pressure to a wound." He used this on Martin, who then told him what he wanted to know. (TV: Countrycide)
On Earth in 16087, the Sontaran Styre experimented on humans to assess their physical limitations. These experiments frequently involved torture. (TV: The Sontaran Experiment)
On Pluto in the far future, lawbreakers were tortured in the Correction Centre. (TV: The Sun Makers)
On Ribos, Binro implied that he was tortured until he recanted his "heresy." (TV: The Ribos Operation)
The Shadow tortured Romana while interrogating her. (TV: The Armageddon Factor)
George Cranleigh was tortured by a South American tribe for stealing a black orchid. (TV: Black Orchid)
On Varos, torture of dissidents in the Punishment Dome was not only legal, it was broadcast to the population as entertainment. This practice was ended by the Governor of Varos, with the aid of the Sixth Doctor. (TV: Vengeance on Varos)
Crime lord Julius Grayle tortured the adult Weeping Angel to see if it could feel pain. (TV: The Angels Take Manhattan)
Beth Pernell tortured Visteen Krane, whom she had murdered but had survived as a creature of pure sound. (AUDIO: Whispers of Terror)
In an alternate timeline, Nigel Rochester tortured the last Dalek. (AUDIO: Jubilee)
In the Vault, Henry van Statten tortured the last Dalek to make it talk. (TV: Dalek)
On Starship UK, the star whale transporting it was tortured to keep it moving. It was later revealed that this had been completely unnecessary, as the whale had wanted to transport the ship. (TV: The Beast Below)
The crew of the Teselecta tortured war criminals who had escaped justice during their lifetimes. (TV: Let's Kill Hitler)
Gray, the brother of Jack Harkness, was tortured for years by an alien race who had invaded the Boeshane Peninsula. (TV: Exit Wounds)
John Harrison tortured his Skullion slaves to keep them under control. (TV: The Man Who Never Was)
The Sontarans operated their own torture chambers. (COMIC: Terrorformer)
After the Spy Master killed everyone on Gallifrey, he planned to put a torture room in the cellar of The Citadel. (TV: The Timeless Children)