Vortex manipulator

A vortex manipulator was a form of basic time travel used by the Time Agency of the 51st century. It is a part of Time Agency wrist strap.

Functions
The vortex manipulator allowed the user to travel through time using the Time Vortex. (DW: Utopia, The Sound of Drums)

Under normal circumstances, it can allow travel of a distance of nearly 200,000 years. (DW: The Parting of the Ways, TW: Everything Changes) Following modifications with a sonic screwdriver, it could allow travel from the End of the Universe to the 21st century. (DW: The Sound of Drums)

The Doctor considered it very primitive compared to a TARDIS, describing his TARDIS as a "sports car" to Jack Harkness's "space hopper". He also described it as "cheap and nasty time travel, very bad for you", and that he was "trying to give it up". (DW: The Big Bang)

Abilities
Presumably, the vortex manipulator created some sort of shield to protect an Agent from the side effects of an unprotected journey through the vortex. This did not, however, prevent the infliction of considerable discomfort for the user, as shown by the Doctor, Jack and Martha's responses upon arriving in London. (DW: The Sound of Drums )

Jack's admission that he was unable to reach his intended destination (DW: Utopia ) when returning to Earth's past would seem to imply that vortex manipulators are not reliable forms of exact time travel, certainly when compared to a TARDIS. This appears to be backed up by his surprise that the trip back from Utopia via the manipulator brings them back so close to when they left, which something the Doctor takes credit for. This may be due to the Doctor's time related abilities or the Doctor's repairs to it with his sonic screwdriver. However, when River Song and the Eleventh Doctor used one to travel through time and space, they seemed to experience no trouble, although it's possible that it was a more recent moddel compared to the one Jack Harkness has. (DW: The Sound of Drums, The Pandorica Opens, The Big Bang)

The vortex manipulators were very resilient, and one was able to survive a bomb that would destroy a Human. (TW: Children of Earth: Day Five)

Time Agents were given a vortex manipulator. Jack Harkness had his manipulator housed in a Time Agency wrist strap. (DW: Utopia) Although it was generally used by the Agency, the Family of Blood stole one to follow the Doctor around the universe. (DW: Human Nature / The Family of Blood) The TARDIS controls include a vortex manipulator. (DW: Attack of the Graske)

When Gray invaded the Torchwood Hub he used his manipulator and it seemed to have a function where all Weevils in Cardiff go rabid. (TW: Exit Wounds)

Jack used information from the UNIT Project Indigo to teleporter (based on Sontaran teleport pod technology) to reactivate the teleport function on his vortex manipulator in ; this suggests that vortex manipulator technology may derive its origins from earlier Earth-based projects such as Project Indigo.

When traveling through time with a vortex manipulator, the traveler seems to use both the teleport function and time travel function depending on where they want to go. For example, when the Doctor, Martha and Jack traveled from the End of the Universe, they left from an alien planet and ended up on Earth. This indicates that the manipulator likely has a long teleport range. 

The vortex manipulator was used to transport The Pandorica into the heart of the explosion of the TARDIS. After being brought back by Amy, The Doctor gave the vortex manipulator back to River Song who used it to time-travel or teleport away.

Other uses

 * Communication between users, listening to radio broadcasts, including storage of messages (TW: Kiss Kiss, Bang Bang, DW: The Sound of Drums)
 * Projection of holograms (DW: The Empty Child, TW: Kiss Kiss, Bang Bang, Fragments)
 * Teleportation (DW: The Sound of Drums, Last of the Time Lords, The Stolen Earth Children of Earth)
 * Tracking of life signs (DW: Journey's End, Bad Wolf)
 * Remote control of electronic devices (TW: Everything Changes, Exit Wounds)

Owners

 * Captain Jack Harkness
 * Captain John Hart
 * Gray (possibly stolen)
 * The Family of Blood (stolen)
 * Mairwyn (Mexico time rift flotsam)
 * Dorium (from dead Time Agent)
 * River Song (acquired from Dorium)
 * The Doctor (used after the TARDIS had been destroyed, gotten from River Song)