Teleportation

The act of teleportation.

Teleportation is a form of matter transmission and can be one of either a process of physical/psychological will or a technological interaction.

Physiological teleportation

The Kitlings and those affected by the Cheetah World could teleport away from their home to hunt for prey, and then return through what was a physical (or possibly psychological/instinctual) process. The ability could also be transferred as Ace, Midge, the Master and the Doctor all acquired the ability, although it was not permanent in the majority of those who were affected. (DW: 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. (DW: Planet of the Spiders)

Technological teleportation

In the case of a technological process, Clockwork Droids possessed a short-range teleporter (DW: The Girl in the Fireplace) and Lady Cassandra O'Brien possessed a long-range teleporter, although her use of teleportation was forbidden under Peace Treaty 5.4/Cub/16. (DW: The End of the World)

Also, in the case of teleportation through technology, a signal is needed for the teleport to work. The signal needs to be broadcast close to the person or item being teleported. The signal can also be reworked to teleport a person back after they had teleported away. (DW: The End of the World, Boom Town).

The planet Sto (or at least Max Capricorn Cruiseliners) also has a form of teleportation, the full range of which is unknown, however it’s range is at least enough to teleport from a ship in orbit to the Earth’s surface. It uses bracelets, which can detect whether any mishap has befallen the wearer, and can signal the system to hold the molecules of the wearer in stasis as a safety feature. The wearer can then be brought back to the ship, provided that their pattern has been stored in the buffers. (DW: Voyage of the Damned)

Teleportation when power is low can result in an incomplete transfer causing part of units to not materialise. (NSA: The Pirate Loop)

Sontarans had to use pods at areas for dematerialisation and rematerialisation. (DW: The Sontaran Strategem / The Poison Sky)

Captain Jack Harkness's Time Agent Wrist Strap contained a teleport as well. The Doctor, Martha and Jack used it to teleport to the Valiant and Martha later used it to escape the Master. (DW: The Sound of Drums)

It was taken from her by him later and he teleported to Earth with it to try to force the Doctor to stop, but the Doctor called his bluff and later teleported them back to the ship. The Doctor deactivated the wrist strap's ability to teleport and travel through time. (DW: Last of the Time Lords)

Jack was able to re-initialise the teleport function with a missing bit of information gleaned through Project Indigo thanks to Martha. Jack then teleported with it to the Doctor and the TARDIS. UNIT created Project Indigo using Sontaran technology to create a teleporter of their own. Martha Jones managed to use this experimental teleporter to escape UNIT's headquarters when the Daleks attacked and was able to use part of the code in it to help Captain Jack bring his own teleport back online. The Doctor disabled it again after the crisis was over however. (DW: The Stolen Earth / Journey's End)

At some point, Jack apparently got his teleport working again as at the end of Children of Earth, he is able to teleport to a cold fusion crusier nearby in the solar system to start a new life. His teleport seems to have a very long range however, as he stated that that ship was at the edge of the solar system and that's the furthest teleport done on the series.