Time travel
Time travel was, as the name suggested, the process of travelling through time, in any direction. In the 26th century, individuals who time travelled were sometimes known as persons of meta-temporal displacement. (PROSE: The Mary-Sue Extrusion) The Eleventh Doctor compared time travel to "a tear in the fabric of reality". (TV: The Name of the Doctor)
Methods
Technological or biotechnological methods
By space-time vessel
The Time Lords were able to achieve time travel after Omega converted a star into a black hole. (TV: The Three Doctors) They used the Eye of Harmony thereafter to power their civilisation and power their time travel facilities from TARDISes to the extraction chambers which could pluck individuals out of the timeline safely before they died. (TV: The Deadly Assassin, Doctor Who, Journey to the Centre of the TARDIS, Hell Bent) By his ninth and tenth incarnations, the Doctor also used the Cardiff rift to "soak up" its radiation for his TARDIS to use. (TV: Boom Town)
The Third Zone scientists Kartz and Reimer built a primitive time machine modelled on Time Lord technology. It almost worked, but ultimately only made one successful trip before it was destroyed. It needed a Time Lord's Rassilon Imprimatur to work properly. (TV: The Two Doctors)
On Earth, the first pioneer in the field was Orson Pink in the early 22nd century, whose first trip accidentally brought him to the end of the universe. (TV: Listen) Hila Tacorien, great-great-great-great-great-granddaughter of a couple from the 20th century, was a human pioneer explorer of time, who accidentally got lost in a pocket dimension. (TV: Hide)
Magnus Greel used an experimental time cabinet based on 51st century human technology. (TV: The Talons of Weng-Chiang)
The Imperial Daleks under Davros, who already had limited time travel technology, expected to obtain equivalent time travel to the Time Lords by stealing the Hand of Omega and replicating their process on Skaro's sun. (TV: Remembrance of the Daleks)
Osmic projection was a means of time travel used by the Sontarans. The Third Doctor referred to it as rather limited in its temporal range when used by the Sontaran scout. (TV: The Time Warrior)
Time Scoop technology enabled the user to transport other people and objects remotely. Without any ally on the other end, it could leave the user stranded in another time period with no way to return. (TV: Carnival of Monsters)
Time corridor technology was used by the Daleks, (TV: The Evil of the Daleks, Resurrection of the Daleks, Remembrance of the Daleks, Victory of the Daleks) Osirans, (TV: Pyramids of Mars) the Borad (TV: Timelash) and the Ra'ra'vis. (COMIC: Time Fraud)
A kind of time viewer, called a quantum imager, enabled one to observe and (to a limited degree) communicate with people in the past. (PROSE: The Least Important Man)
Pushing energy into a warp drive could create a time window. (TV: The Girl in the Fireplace)
A warp drive accident fractured one individual, Scaroth, into "fragments" scattered through various eras of time and linked by telepathy. (TV: City of Death) Another warp drive accident had the effect of propelling the vehicle in question roughly sixty-five million years back in time. (TV: Earthshock)
A rift manipulator could be used in conjunction with the temporal rift itself. (TV: Captain Jack Harkness, End of Days)
A vortex manipulator was a crude time travel device. It could miss by hundreds of years and broke down easily. It was referred to by the Tenth Doctor as more of a "space hopper" compared to the TARDIS. (TV: Utopia)
Emergency temporal shift was a form of time travel used by the Cult of Skaro to escape being sucked into the Void, and was later used by Dalek Caan to escape from 1930s New York City. (TV: Doomsday, Evolution of the Daleks)
At some point after the Last Great Time War during which the Time Lords deceived the universe into thinking they were extinct barring the Doctor, the Time Lords sent Missy and Yayani to the Kyme Institute where Doctor Kalub had been experimenting with genetically engineering a whole new creature with time and space travel ability and then imprisoning it within a stasis field. The energies were then harnessed for perpetual energy for time travel. Kalub died, but the creature itself was imprisoned within Missy's TARDIS. (PROSE: Lords and Masters)
Teri Billington's time dilation project allowed the Sentinels of the New Dawn to achieve time travel. After some adjustment by the Third Doctor, her particle accelerator took him and Liz Shaw to 2014. Upon returning, Liz disassembled Billington's particle accelerator, preventing the Sentinels from discovering time travel. (AUDIO: The Sentinels of the New Dawn)
Mirrors
Time travel by use of mirrors was based on the principle that mirrors reflect light and time travel is moving faster than light. If static electricity was passed through the mirrors, more than images could be reflected and whole objects could be sent back in time. As well, certain trace elements in the machine, like taranium, were also needed. (PROSE: The Wheel of Ice)
Edward Waterfield and Theodore Maxtible attracted the attention of the Daleks while experimenting with static electricity and mirrors. (TV: The Evil of the Daleks)
The mysterious Gateway situated in the void between N-Space and E-Space provided access to different times and realities, sometimes through mirrors. (TV: Warriors' Gate)
General Mariah Learman and Professor Osric succeeded briefly in making a functioning time machine with over 100 clocks and 1000 mirrors in her prime ministerial house. The act of measuring time changed time and therefore time could be manipulated. The mirrors were coated in orthopositronium, a material where the positron and the electron orbited each other in the same direction. It briefly worked when the Daleks' ship ran aground in the Time Vortex and they homed in on it and made it work. It needed chronons to work, which were sourced when the Eighth Doctor's companion, Charley, held the master clock. It took her and Viola Learman to William Shakespeare's time. This ceased to function when Charley entered the Doctor's TARDIS. (AUDIO: The Time of the Daleks)
A time machine was created by UNIT with the help of Rose Tyler and the dying TARDIS to send Donna Noble back from a universe the time beetle created. (TV: Turn Left)
The Arkive tried to create a mirror-based time machine, but didn't have the necessary parts or skills to make it (PROSE: The Wheel of Ice)
By psychic power or other natural ability
The Eight Legs could teleport as easily through time as through space. K'anpo Rimpoche, a highly advanced Time Lord with great mental discipline, could do the same. (TV: Planet of the Spiders)
The enigmatic Bilis Manger could also also teleport at will through both time and space. This ability was only seen in the vicinity of the Cardiff Rift however. (TV: Captain Jack Harkness, End of Days)
Fenric could transport other living beings via time storms. The people displaced by the time storm often believed they had caused the time storm themselves. (TV: Dragonfire, Silver Nemesis, The Curse of Fenric)
The Fairies could travel through time and space naturally. (TV: Small Worlds)
The Weeping Angels had the ability to send others back in time with a touch. (TV: Blink)
The Trickster, prior to manifesting as a corporeal being, could traverse time and space with ease, though not at any given moment. (TV: Whatever Happened to Sarah Jane?, The Temptation of Sarah Jane Smith)
The Androzani trees travelled through the Time Vortex by using Madge Arwell as a host. (TV: The Doctor, the Widow and the Wardrobe)
By space-time anomaly
The Tharils "rode the time winds". (TV: Warriors' Gate)
A warp ellipse could possibly make time travel possible. (TV: Mawdryn Undead)
Travel via time rift was possible. The Weevils arrived on Earth via this method, (TV: Everything Changes) as did a human aeroplane, the Sky Gypsy. (TV: Out of Time) During rare "negative spikes", the Rift also occasionally abducted random people in time and space from Earth, and disastrously attempted to correct itself. (TV: Adrift)
Sarah Jane Smith acquired a Time Converter which allowed her to open and close time fissures, but these usually only linked two particular places in time. (TV: The Temptation of Sarah Jane Smith)
Both the Great Intelligence and Clara Oswald time travelled by entering the Doctor's time stream from his tomb, both becoming splintered in time. Clara was retrieved by the Eleventh Doctor, while Madame Vastra presumed the Intelligence to have been killed. (TV: The Name of the Doctor)
The Tenth Doctor, in order to defeat some surviving Cybermen from the Battle of Canary Wharf created a space-time portal to the Jurassic era by linking the Cybermen's teleportation equipment to the TARDIS and then setting the portal to open at the last place in time the TARDIS departed from. This linked the two eras together and allowed a Tyrannosaurus Rex to partially emerge in the present and destroy two Cybermen. The Doctor closed the portal when he pulled the main power cable and told Martha Jones that creating one was simple and was something he played with a lot while in school. (PROSE: Made of Steel)
Professor Whitaker, who was fascinated with the idea of time travel, used time eddies in order to transport dinosaurs to modern London. This was done as a part of Operation Golden Age, which consisted of first using the dinosaurs to evacuate London and then rolling back time via the time eddies to colonise the Earth's past before mankind was born in order to replace mankind's history with a new, better civilisation free of corruption and pollution. However, after the Third Doctor reversed the polarity of Whitaker's machine, the scientist and his accomplice Charles Grover were teleported through time, possibly to their "Golden Age", as the Doctor believed. (TV: Invasion of the Dinosaurs)
Blending in
The First Doctor normally hid his clothing with a large cloak, while he and his companions pilfered appropriate garments. (TV: The Aztecs, etc.) However, from at least his third incarnation onwards, he forwent wearing the correct clothing himself. The Eleventh Doctor claimed to be a "temporal chameleon" able to blend into any point of time despite what he wears; companion Rory Williams was annoyed that he and Amy would have to wear togas for visiting Athens when the Doctor didn't. (COMIC: The Chains of Olympus)
Other references
The Aja'ib contained tales involving time travel. (PROSE: Bafflement and Devotion)
Behind the scenes
In General Relativity, travelling to the future is somewhat easy, if you stay near a massive body or travel fast enough. However, travelling to the past is impossible unless you live in a universe with an exotic geometry or some form of exotic matter. These could allow closed timelike curves, due to something like the Tipler cylinder.
