Hacking was the act of gaining unauthorised access to data banks and computer terminals.
Mickey Smith was skilled at this, hacking into John Lumic's Cybus Industries (TV: The Age of Steel) and also hacked into UNIT and the Royal Navy with the Ninth Doctor's help to launch a missile on 10 Downing Street. (TV: World War Three) He was so skilled that he hid himself online to search for information about the Doctor, keeping himself hidden for a year. (TV: Aliens of London)
The Doctor was also a skilled hacker, demonstrating prestigious skill with computers on multiple occasions, particularly during their eleventh incarnation. (TV: The Eleventh Hour, The Bells of Saint John) The Twelfth Doctor also hacked all the cameras on Earth, switching them off to discover which biochemical research centre the Monks were watching (TV: The Pyramid at the End of the World) and also hacked the database on a Mondasian colony ship, rapidly redefining the definition of humanity for the Cybermen aboard to foil the Saxon Master's plans. (TV: The Doctor Falls) Nardole, having dubbed himself the "computer guy", (TV: World Enough and Time) was also a proficient hacker, hacking into the same colony ship's fuel lines to remotely detonate them. (TV: The Doctor Falls)
The Doctor sometimes made use of their sonic screwdriver to hack into systems quickly. (AUDIO: The Harvest, PROSE: Seeing I, TV: The Runaway Bride, The Hungry Earth)
Clara Oswald and her counterparts were skilled hackers. Oswin Oswald managed to hack into the Daleks Pathweb and deleted all memory of the Doctor within seconds, a feat the Doctor himself admitted he couldn't do despite trying for years. (TV: Asylum of the Daleks) Clara herself gained capable hacking skills after being uploaded into the Great Intelligence's data cloud, using them to hack into the Shard's computer networks to disrupt their work and take pictures of them using their web cameras. Control of the data cloud also allowed Rosemary Kizlet to hack her staff. (TV: The Bells of Saint John)
Jorjie Turner hacked the criminal activity file of "Stark Reality", finding that his real name was Starkey. (TV: Regeneration)
The Wikipedia page about Amble the Ugly Doll was often hacked and altered. (PROSE: Writer's Notes)