Psychic power

Psychic powers, also known by the acronym ESP for Extra-Sensory Perceptions (TV: Planet of the Spiders), were made possible by the conscious or unconscious manipulation of psychic energy.

History
Originally related to magic and still understood as such in many cultures, psychic abilities survived the Time Lords' imposition of the laws of physics on the universe by being sufficiently grounded in science. (PROSE: So Vile a Sin)

The Tenth Doctor described psychic abilities as simply, "the ability to see strands of future time." (PROSE: The Weeping)

The Soviet Union began research into psychic powers before World War II in the hope of creating a psychic bomb designed to provoke extreme emotions in people. This ambition had been achieved by 1965. The United States of America also researched psychic powers in the 1960s. (AUDIO: Peshka)

Natural racial abilities
Some species were innately psychically active - in some cases it was very unusual for an individual of a given species not to manifest psi-powers. These powers could be of any type - for instance, the Arcateenians appeared to be innately telepathic. (TV: Greeks Bearing Gifts)

A Krynoid and Harrison Chase developed a psychic attachment, with Harrison being indoctrinated with the others thoughts. (TV: The Seeds of Doom)

The Doctor and Susan Foreman  both displayed telepathic abilities, but most Time Lords did not. Several other Time Lords  did show psychic abilities and the Doctor  said at least twice  that Time Lords were telepathic.

Innate psychic ability in humans was rare, but not unknown: according to the Third Doctor, they were just dormant in most members of Homo sapiens. (TV: Planet of the Spiders) Most humans had at least some latent psychic potential. Significant individuals (such as William Shakespeare), showed enough latent psychic ability to see psychic paper as blank. (TV: The Shakespeare Code) This ability may have been due to an extra synaptic engram in the brain, which was seen in individuals with mild telepathic abilities such as Tim Latimer. Torchwood 1 personnel were given basic psychic training, also giving them this ability. (TV: Army of Ghosts)

The Pyroviles had psychic powers, as well. They were able to give them to humans and did so to the Sibylline Sisterhood. (TV: The Fires of Pompeii)

Mutation due to external factors
In species that were not normally psi-active, powers could nevertheless still appear given the right stimuli. Humans living near a time rift developed psychic abilities, (TV: The Unquiet Dead, The Fires of Pompeii) which might vanish if the rift were sealed. (TV: The Fires of Pompeii) Prolonged exposure to a Metebelis crystal might also result in psychic powers.

Due to living on the lip of a wormhole for centuries, human colonists on Agelaos developed psychic abilities. (PROSE: The Weeping)

Sensory abilities

 * Telepathy
 * Clairvoyance (also known as Extra-Sensory Perception)
 * Precognition
 * Psychometry
 * Time-sensitivity: the ability to sense disruptions in time and/or reality, or to detect that a given object or person was displaced in time.
 * Empathy

Manipulative abilities

 * Telekinesis
 * Mind control

Artificial psychic phenomena
Psychic energy was normally only produced by living minds, which made it (and the powers utilising it) difficult to study or replicate using conventional technological means.

However, a number of devices were constructed to facilitate or mimic natural psychic powers. TARDISes generated a psychic field and incorporated telepathic circuits to facilitate both short- and long-range communications. (TV: Frontier in Space) The IRIS Machine artificially boosted the telepathic potential of human test subjects. (TV: Planet of the Spiders) The Arcateenians used telepathy pendants for long-range communication. (TV: Greeks Bearing Gifts) The Coronet of Rassilon gave the wearer the power of mind control, even over multiple subjects simultaneously. (TV: The Five Doctors)

In his later incarnations, the Doctor routinely carried psychic paper to save time in establishing his credentials. (TV: The End of the World, The Long Game and others) This ploy was also used by Captain Jack Harkness. (TV: The Empty Child) Psychic credit cards were used by the Doctor to hold money. (PROSE: Only Human)