Psychic paper

Psychic paper was a blank, white card that had special properties. When shown to a person, it could usually induce them to see whatever the user wished them to see printed on it. However, it proved useless on geniuses such as William Shakespeare (TV: The Shakespeare Code) or those with feeble imaginations, such as Fenton. (TV: Flatline)

It was often used by the Doctor, in later incarnations. The Doctor's psychic paper served as a "get-out-of-jail-free card", allowing them to avoid many setbacks, by gaining entrance, confidence or trust.

Users
The Second Doctor was given psychic paper while employed as an agent by the Time Lords' covert organisation, the Celestial Intervention Agency, which had developed the technology. (PROSE: World Game) The Eighth Doctor carried it on a few occasions. (AUDIO: The Turn of the Screw, The Starship of Theseus) The War Doctor used it in the Last Great Time War, (AUDIO: Legion of the Lost) but preferred the feel of a gun in his hands. (COMIC: The Organ Grinder)

The Doctor, in their ninth, (TV: The End of the World) tenth, (TV: New Earth) eleventh (TV: The Eleventh Hour) and twelfth incarnations, (TV: Listen) habitually carried it, as did Captain Jack Harkness during his rogue days. Jack said that the paper was a new technology put into use by the Time Agency which had employed him. (TV: The Empty Child)

At least some Weeping Angels had access to psychic paper, which according to the Eleventh Doctor, was "child's play" for them. (PROSE: Touched by an Angel)

Properties
Usually, it showed what the holder of the paper wanted the person reading the paper to see, (TV: The End of the World) or vice-versa. (TV: The Idiot's Lantern) Messages on psychic paper appeared in the reader's handwriting. (PROSE: Touched by an Angel) The message could also be signed with a kiss, something Donna teased the Tenth Doctor about. (TV: Silence in the Library) It could even be used to open doors in place of a keycard (TV: Army of Ghosts) and the Tenth Doctor once used it in lieu of an Oyster card to pay before boarding a bus in London. (TV: Planet of the Dead) It could also be used like a credit card; Amy told the Eleventh Doctor to hand her the psychic paper when they landed in New York so she could go shopping. (PROSE: The Forgotten Army) Mischief-making Courtney Woods swiped it, also using it to shop, and as a fake ID to get into clubs. (TV: Kill the Moon)

Psychic paper could receive messages from beings with sufficient psychic ability, no matter where the Doctor was in time and space, such as the Face of Boe, (TV: New Earth) the Atraxi, (TV: The Eleventh Hour) Tenzas, (TV: Night Terrors) and, to his initial surprise, River Song. (TV: Silence in the Library, GAME: The Eternity Clock) The Doctor explained this function to Amelia Pond as taking "a dandy little message" when the Atraxi sent him a message, warning about Prisoner Zero's escape. (TV: The Eleventh Hour) Kate Stewart and UNIT managed to contact the Doctor through the psychic paper. (TV: The Power of Three)

Time Lords like the Doctor could psychically connect with the paper. He did this to lead Amy to where he was being held captive by Vykoids. However, the link was faulty and lingered even after the Doctor didn't need it. (PROSE: The Forgotten Army) When used by an individual with psychic powers, the psychic paper would sometimes bounce the individual's powers back on them. When used by Waechter, it allowed him to see his own future. (PROSE: The Weeping) It could also display text messages from mobile phones the Doctor upgraded to allow communication with him and the TARDIS. (COMIC: The Fountains of Forever)

The Tenth Doctor also once used the psychic paper as a truth telling device by having Constantine Ethelred Gurney hold the blank paper and then reading off who he was, where he was from, his crimes, and his Volag-Noc release date. (TV: The Infinite Quest)

The Eleventh Doctor at some point set his psychic paper to Temporal News Feed, and was alerted via the sound of a horn honking. (TV: Dinosaurs on a Spaceship)

According to the Twelfth Doctor, if there was any trouble at the Vault he would receive a message on his psychic paper. (TV: The Pilot)

Limitations
In the hands of untrained users, the paper was prone to displaying facts they subconsciously wanted the reader to be aware of. This could be quite embarrassing, such as in Rose Tyler's case. (TV: The Empty Child)

When the intended thought was too unbelievable, the psychic paper would only display wavy lines. The Eleventh Doctor explained that such a lie — in his case, that he was universally recognised as a mature and responsible adult — shorted it out because it was "too big". (TV: A Christmas Carol)

The paper did not work on people of genius, such as William Shakespeare, making him the first person the Doctor met who was naturally immune to it, (TV: The Shakespeare Code) or on people who had "a serious lack of imagination." (TV: Flatline) It also didn't seem to work on some species, such as Saturnynians. (TV: The Vampires of Venice)

The psychic paper did not work on humans whose minds had already been manipulated by another source. The minds of the inhabitants of a 1982 nuclear bunker were manipulated by giant cockroaches, so the psychic paper did not work on them. (AUDIO: Day of the Cockroach)

The "basic psychic training" that was standard at Torchwood One was enough to distinguish psychic paper from real. (TV: Army of Ghosts)

When wet, the psychic paper acted rather differently and was unable to translate the Tenth Doctor's thoughts properly. (PROSE: Wetworld)

When a parking inspector signed the Eleventh Doctor's psychic paper, he believed it wouldn't work, until Amy Pond turned it around the other way, causing messages to appear back to front. (PROSE: Apollo 23)

One could distinguish psychic paper from real paper by looking for "fractal lines" on the former. (TV: A Good Man Goes to War)

The paper could also only work effectively on civilisations that had invented writing — when the Eleventh Doctor attempted to use it in the Viking era it remained blank before eventually displaying an image of a rabbit (of which there were thousands around), implying that he was a "Rabbit Inspector". (PROSE: Dark Horizons) If a civilisation had the concept of writing, the paper could work on a level beyond written language, such as one man being able to read the message on it even when he himself was illiterate. (PROSE: The Silent Stars Go By)

Not everyone was affected by the psychic paper. People, or groups, known to be immune to its illusions included Torchwood One personnel, due to psychic training; (TV: Army of Ghosts) William Shakespeare, apparently due to his incredible mind; (TV: The Shakespeare Code) Ernest Shackleton, due to how determined he was; (COMIC: The First) Eve; (PROSE: The Last Dodo) Morret and other veterans of the Telepath Uprising; (PROSE: Judgement of the Judoon) GateBots; (COMIC: Attack of the GateBots!) Rosanna Calvierri; (TV: The Vampires of Venice) Frederick Abberline; (COMIC: Ripper's Curse) Stella; (PROSE: Prisoner of the Daleks) the Anglican Marines of the Church, who trained themselves for the Battle of Demons Run; (TV: A Good Man Goes to War) Ood; (COMIC: Psychic Paper Inc Claims Department) a community service officer, due to having a highly unimaginative mind; (TV: Flatline) and Field Marshall Erwin Rommel. (COMIC: The Instruments of War)

Behind the Scenes
Carta psichica
 * In The Woman Who Fell to Earth, the Thirteenth Doctor said she lost everything in her pockets when she fell out of the TARDIS. This may have likely included the psychic paper, as the Doctor is known to almost always carrying the psychic paper with them at all times.

Papier psychique