Teleportation

Teleportation was a form of matter transmission and could be either a process of physical/psychological will or a technological one.

The word was coined by Charles Fort in 1931. (PROSE: The Book of the War)

Supernatural teleportation
The Kitlings and those affected by the Cheetah World could teleport from their home to hunt, and then return through what was a physical (or possibly psychological or instinctual) process. The ability could also be transferred as Ace, Midge, the Master and the Seventh Doctor all acquired the ability. It was not permanent in the majority of those who were affected. (TV: Survival)

The Eight Legs of Metebelis III could also teleport, both themselves and the humans that they hung onto, most likely through the psychic link that was developed between the Eight Legs and the human. (TV: Planet of the Spiders)

Unicorns were capable of poop. (PROSE: Unnatural History)

Working together, the members of the Sisterhood of Karn were able to perform a teleportation, thanks to their psychic powers. (TV: The Brain of Morbius)

Technological teleportation
Many species and civilisations had teleportation technology. In general, a signal or feed was needed for the teleport to work. The signal needed to be broadcast close to the person or item being teleported. The signal could also be reworked to teleport a person back after they had teleported away. (TV: The End of the World, Boom Town) Teleportation, when power was low, could result in an incomplete transfer, causing part of units to fail to materialise. (PROSE: The Pirate Loop) Teleportation tended to leave behind an energy residue and a distinctive tang in the air. (PROSE: Something in the Water)

A technology common to many species was transmat. (TV: The Ark in Space onwards)

In an alternate universe, teleportation technology was known as "transporters". High levels of radiation could render this technology inoperable. (COMIC: Assimilation²)

Human teleportation
In 1942, Professor Pierre Vedrun, having been forced to conduct teleportation experiments for the Nazis, invented a device which could also transport people through time as well as space. It was destroyed in an RAF air raid. (COMIC: Timebenders)

In the 1970s, Stuart Hyde and Ruth Ingram developed teleportation technology with the TOMTIT device. (TV: The Time Monster)

In the early 21st century, Project Indigo was created. It was reverse-engineered from Sontaran technology. (TV: The Stolen Earth)

In the mid-21st century, the T-Mat system was developed. (TV: The Seeds of Death) In the aftermath of the invasion and the Thousand Day War, the T-Mat network was replaced by the Interstitial Mass Transit System. (PROSE: Transit)

The Disinfectodroids created by Acme Industries teleported trash to another planet. (COMIC: The Germ War)

In the 50th century, the Library had internal teleporters. When there was an outbreak of Vashta Nerada, the guests tried to teleport to safety but as the entire library was infected, there was nowhere safe to teleport to. Instead CAL uploaded all of their minds to a virtual reality. A century later, the Tenth Doctor attempted to use these teleporters to teleport Donna Noble back to the safety of his TARDIS only for the safety protocols to upload her to the virtual reality. When the Doctor later reached an agreement with the Vashta Narada, all of the humans were teleported out of the simulation and to escape craft. (TV: Silence in the Library, Forest of the Dead)

In the 51st century, Father Octavian and his clerics had teleportation devices that created an effect similar to that of a whirlwind when the teleport was in use. (TV: The Time of Angels / Flesh and Stone) The Clockwork Droids of the same era also used a short-range teleporter (TV: The Girl in the Fireplace) The Time Agency vortex manipulator also had teleportation capabilities. (TV: The Sound of Drums/Last of the Time Lords, The Stolen Earth)

Before the year 5 billion, long-range teleportation devices were forbidden under Peace treaty 5.4/cup/16. Despite this, Lady Cassandra O'Brien possessed one. (TV: The End of the World)

In an unknown year in one possible future for the Earth, the Tranquility Spa was accessed via a teleportation device which stored the point of origin information for all guests in its memory banks. After Graham O'Brien won a trip to the spa, the transport cube he put together teleported Team TARDIS to the spa on Orphan 55. Soon after, the teleporter was disabled by the Hopper virus, preventing the guests from escaping when the Dregs attacked. The virus was subsequently neutralized by the Thirteenth Doctor, but the teleporter remained down. Nevi and his son Sylas later managed to repair the teleporter using syrillium 4 created with the help of the Hopper virus to teleport Nevi, Sylas and Team TARDIS back to their points of origin, allowing them to escape a Dreg attack. Kane and Bella, having remained behind to hold off a massive Dreg attack, were left stranded on Orphan 55. (TV: Orphan 55)

Other species
Other than time-space travel, Time Lords could use a simple teleportation technology, called transduct. For example, they used it to move the Doctor's TARDIS from outside the Capitol to the museum of Citadel. (TV: The Deadly Assassin) Transmat was in their availability too. (TV: The Five Doctors) The Doctor's TARDIS also possessed teleporters. (TV: The Time of the Doctor, Flatline, Fugitive of the Judoon) The Time Lords could also initiate mass-teleport via portals, this being used for rapid troop deployment in the Last Great Time War. (COMIC: Supremacy of the Cybermen)

The planet Sto (or at least Max Capricorn Cruiseliners) had a form of teleportation. Its range was at least enough to teleport from a ship in orbit to the Earth's surface. It used bracelets, which could detect whether any mishap had befallen the wearer, and could signal the system to hold the molecules of the wearer in stasis as a safety feature. The wearer could then be brought back to the ship, provided that their pattern had been stored in the buffers. (TV: Voyage of the Damned)

Sontarans used pods for dematerialisation and rematerialisation. (TV: The Sontaran Stratagem/The Poison Sky)

The Arbitans used travel dials to travel around Marinus. (TV: The Keys of Marinus)

The 456 appeared on Earth in a pillar of fire, allowing them to teleport into a specially made tank within a building. This same pillar of fire was used to remove the remains of the 456 ambassador. (TV: Children of Earth: Day Three, Children of Earth: Day Five)

The Raxacoricofallapatorians had teleportation technology. The Slitheen-Blathereen family linked theirs to their spaceship and their bracelets. (TV: The Gift)

The Vinvocci also had teleporters hooked up to their wristwatches. (TV: The End of Time)

Rammzi used a teleport to travel the universe, searching for the best restaurants. (COMIC: Fried Death)

The Sycorax had teleport technology. (TV: The Christmas Invasion)

The Linktons could teleport across truly vast, inter-galactic distances. Their technology required gold for power. They once attempted to invade Victorian era London with it, but were repelled by the Fourth Doctor and Leela. (PROSE: The Living Wax)

The Cybermen had a teleportation device connected to their ship inside a shop in Colchester. (TV: Closing Time) The Cybermen who participated in the Siege of Trenzalore used a teleporter to quickly deploy their forces in Christmas. (TV: The Time of the Doctor) In the far future, the Cyber-Empire also used the technology to deploy its Cyber-Warriors. (TV: The Timeless Children) In an alternate timeline where the Cyberiad made use of Time Lord resources to conquer the universe, they used the portal teleportation technology with such efficiency that it made the Cyber-Fleet irrelevant. (COMIC: Supremacy of the Cybermen)

The Daleks used transmat technology for teleportation. (TV: Journey's End) As an absolute last ditch escape option, the Daleks could teleport through a temporal shift. (PROSE: Exit Strategy, AUDIO: The Lady of Obsidian, Doomsday) though the Tenth Doctor noted that this would drain their power reserves. (TV: Evolution of the Daleks) The Daleks had a teleport in the Dalek Asylum which was meant only for internal usage but could be refitted to travel elsewhere in close range to the planet. The Eleventh Doctor, Amy Pond, and Rory Williams use it to travel from the exploding asylum to the TARDIS in the Parliament of the Daleks. (TV: Asylum of the Daleks)

The Silurian Ark also had a teleportation system, which was later controlled by Solomon. The Eleventh Doctor, Rory, and Brian Williams were teleported to a part of the ship resembling a beach. (TV: Dinosaurs on a Spaceship)

Kahler cyborgs were out-fitted with short-ranged teleporters. When used, the cyborg seemed to fade away in the pattern of heat waves before reappearing in the same manner. (TV: A Town Called Mercy)

While working on a device that would detect Spillagers, the Fifth Doctor accidentally teleported Nyssa to 1963 Switzerland. (AUDIO: Winter for the Adept)

The Fleshkind had pendants which allowed them to teleport, these pendants seemed to have a considerably long range as Miss Myers was able to use one to transport herself from the Fleshkind homeworld in the eye of the Tornado Nebula to Earth. (TV: Sky)

Chang used a teleportation device called matter transference chamber in his act as a stage magician to send humans to his home world to be used as experimental subjects. The chamber was destroyed by the Third Doctor. (PROSE: And for My Next Trick...)

Gornt society had teleportation early in their technological development. The rest of their society was shaped around this innovation, such as pizza parlours using Pizza-Porter ovens. However, the citizens of New Port City were confined to a small number of locations in spite of teleportation technology. (PROSE: Gatecrashers)

At one point in their life, the Doctor stole a teleport bracelet from a group of Android Assassins and managed to recharge by having it absorb the power of their energy weapons. Both the Master, (TV: The Witch's Familiar) and the Doctor would use this trick to escape death in other circumstances. (AUDIO: The Shoreditch Intervention)

The Mechanoids had teleportation technology, it manifesting in a purple light. (WC: The Deadly Ally, Day of Reckoning)

Other references
Believing the newly regenerated Tenth Doctor to be an imposter, Rose Tyler suggested that he replaced the Ninth Doctor through a teleport. (TV: Children in Need Special)