Black hole

Black holes were regions in space typically created when a star ran out of fuel and collapsed in on itself, creating a singularity due to its strong density and gravitational pull. It was a place where gravity was so great that nothing, not even light or time, could escape its pull. It was often theorised that black holes were gateways into other universes. (TV: The Impossible Planet)

Black holes and Time Lords
Though human astrophysicists thought black holes occurred naturally, the Tenth Doctor once implied that the Time Lords invented black holes. (TV: The Satan Pit)

Omega and Rassilon destroyed the star Qqaba (COMIC: Star Death) to produce an energy source powerful enough to enable time travel. Omega, thought dead, survived his journey through this black hole, although he was trapped within it. He was able to shape matter within it at his will. (TV: The Three Doctors, Arc of Infinity) Rassilon brought back either a black hole or its singularity to become the Eye of Harmony. (TV: The Deadly Assassin)

When two versions of the Doctor's TARDIS collided, the Doctor combined a black hole and a supernova to stop a black hole from being created, after witnessing it in his fifth incarnation. (TV: Time Crash)

The Doctor's TARDIS had the power to both resist the pull of a black hole and to tug the Walker Expedition's rocket out of the black hole's gravitational field. (TV: The Satan Pit)

Effects on the Universe
Black holes could act in two ways: some holes did, as sometimes speculated, lead to other universes and served as portals; other holes just ate and ate and ripped up star systems and anything else. (TV: The Impossible Planet) Black holes could also serve as a gateway into hyperspace. (TV: The Horns of Nimon)

Before the universe began, the ancient Disciples of the Light fixed the planet Krop Tor in geostationary orbit around K37 Gem 5. The Tenth Doctor, before learning of this, regarded the planet's fixed orbit as scientifically impossible. Both the black hole and the planet served as a prison in which to confine the Beast. (TV: The Impossible Planet)

In 2986, the Black Hole of Tartarus presented a hazard to spacecraft. (TV: Terror of the Vervoids)

Artificial Black Holes
Artificial black holes could be created. In 2006 or later, an experiment in Switzerland created an artificial black hole, which the robot K9 spent about three years trying to stabilize in order to protect Earth. (TV: Invasion of the Bane, The Mad Woman in the Attic) In 2009, Ship converted the black hole into fuel, releasing K9 and saving the Earth. (TV: The Mad Woman in the Attic)

Black holes could also be used for transportation. The Nimons based most of their technology on artificial black holes, especially for long distance transportation. (TV: The Horns of Nimon)

During the Year That Never Was, created a fleet of Toclafane rockets, each holding a black hole converter so that he could could wage war on the rest of the universe and turn Earth into 'New Gallifrey' under his control. The rockets faded away when time was reversed. (TV: Last of the Time Lords)

Some time before 2050 the Oroborus destroyed the planet Centauri by siphoning off its future, resulting in the planet being turned into a black hole. (TV: Oroborus)

Minor references

 * An arch-criminal from the planet Nefrin, Brimo, sentenced to remain alive forever in an eternity capsule, found herself inside a black hole when Nefrin's sun collapsed upon itself. Much like Omega, she found herself in a mutable world shaped by her imagination and drained energy from the universe outside it. (DWM: The Time Witch)
 * Before his death, Eugene Jones planned on attending a lecture entitled "Black Holes and the Uncertainty Principle" at Aberystwyth University with his friend Gary. Having found a flyer for the lecture in Eugene's room, Gwen Cooper showed up there and spoke to Gary for questioning. (TV: Random Shoes).
 * There was a black hole in the Casta Pizellus galaxy. (PROSE: I am a Dalek)
 * The Mother of the Family of Blood was jettisoned into the black hole of a collapsing galaxy, trapping her in its event horizon for, relative to her perception, eternity. (TV: The Family of Blood).
 * Whenever the Vigil teleported, they were shown appearing from a tiny black hole. (TV: The Rings of Akhaten)