Tractor beam

The Doctor's TARDIS holds a neutron star in place with a gravity tractor beam. (TV: The Creature from the Pit)

A tractor beam, also known as an anti-gravity beam (PROSE: A Big Hand for the Doctor) was a beam of energy projected from a vessel or device which could tether and pull another object.

Gallifreyan technology

The Doctor's TARDIS

The Fourth Doctor used his TARDIS' gravity tractor beam to hold a neutron star still while Erato used his ship to weave a protective shell around it. In the process, the tractor beam burned out (TV: The Creature from the Pit), remaining inoperative into at least the Doctor's eighth incarnation (PROSE: The Taking of Planet 5).

It had been repaired by the Doctor's tenth incarnation when he used it to save the Sanctuary Base 6 rocket from a black hole. (TV: The Satan Pit)

The Doctor's TARDIS could create a smaller tractor beam with the help of the Master's laser screwdriver. (GAME: TARDIS)

The Doctor's TARDIS also had an anti-gravity spiral that had similar properties to a tractor beam. (TV: Delta and the Bannermen)

Others

The Time Lord Azmael intended to employ a tractor beam to move two minor planets in the same orbit of the planet Jaconda, previously under his protection. The Sixth Doctor made him change his mind, by pointing out the consequences. (TV: The Twin Dilemma)

The Doctor was sent a psychic signal by his future self to fly to Lakertya as a means of encountering an unknown source of radiation which would force him to regenerate and remove the influence of the Nathemus in his mind that he was at the time unaware of and prevent a plot set in motion by the Valeyard from succeeding in the long run. His TARDIS was attacked by the Rani with focused laser beams, which turned out to be the source of the radiation. She then caught the TARDIS in a tractor beam and made it land on Lakertya. (AUDIO: The Brink of Death, TV: Time and the Rani) In another timeline, she attacked the TARDIS during the end of the Doctor's encounter with a pan-dimensional being that had caused him to slowly perish and had not used irradiated lasers. (PROSE: Spiral Scratch)

Other occurrences

During the Last Great Time War, a Dalek ship caught the mining ship Tempest in a tractor beam. (AUDIO: A Thing of Guile) In the final days of the war, the Eternity Circle of the Daleks caught the Doctor's TARDIS in the proximity of the Tantalus Eye with a tractor beam. (PROSE: Engines of War)

Chula warships, such as the one stolen by Jack Harkness, possessed a tractor beam. (TV: The Empty Child/The Doctor Dances)

A Sontaran ship, captured in an alternative Death Zone on Gallifrey, was provided with such a beam. (AUDIO: The Five Companions)

K9 Mark 2 possessed a tractor beam which could pull an object as large as an adolescent humanoid, (TV: Fear Itself) he could also use it to absorb microscopic objects. (TV: Black Hunger)

Soul Pirates used tractor beams to abduct people, particularly children, to harvest them for parts. (PROSE: A Big Hand for the Doctor)