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. (DW: The Shakespeare Code) It was most commonly seen being used by the Doctor in his later incarnations.

Users
The Second Doctor was given psychic paper while employed as an agent by the Time Lords' covert organisation, the Celestial Intervention Agency. The CIA had developed the technology. (PDA: World Game)

The Doctor, in his Ninth, Tenth and Eleventh incarnations, habitually carried it, as did Captain Jack Harkness when Rose Tyler and the Doctor first met him in World War II London. (DW: The End of the World, The Empty Child, New Earth, The Eleventh Hour) Jack said that the paper was a new technology put into use by the Time Agency which had employed him. (DW: 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. (NSA: Touched by an Angel)

Properties
Usually, it showed what the holder of the paper wanted the person reading the paper to see (DW: The End of the World), or vice-versa (DW: The Idiot's Lantern). Messages on psychic paper appeared in the reader's handwriting. (NSA : Touched by an Angel) The message could also be signed with a kiss, something Donna found ridiculous. However, the Doctor explained "we've all done that", implying it was a function he tried before. (DW: Silence in the Library) It could even be used to open doors in place of a keycard (DW: Army of Ghosts) and the Doctor once used it in lieu of an Oyster card to pay before boarding a bus in London. (DW: Planet of the Dead) It could also be used like a credit card; Amy told the Eleventh Doctor to had her the Psychic Paper when they landed in New York so she could go shopping. (NSA: The Forgotten Army)

Psychic paper could receive messages from beings with sufficient psychic ability, no matter where the Doctor is in time/space, such as the Face of Boe, Atraxi, Tenzas, and, to his initial surprise, River Song. (DW: New Earth, The Eleventh Hour, Night Terrors, Silence in the Library) The Doctor explained this funcation to Amelia Pond as taking "a dandy little message" when the Atraxi sent him a message, warning about Prisoner Zero's escape. (DW: The Eleventh Hour)

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. (NSA: 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. (NSA: The Story of Martha: The Weeping)

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's case. (DW: The Empty Child)

When the intended thought was too unbelievable, the psychic paper would only display squiggly 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". (DW: 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 naturaly immune to it. (DW: The Shakespeare Code)

When wet, the psychic paper acted rather differently and was unable to translate the Tenth Doctor's thoughts properly. (NSA: 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. (NSA: Apollo 23)

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

Resistance
Not everyone was affected by the psychic paper. People, or groups, known to be immune to its illusions included:
 * People who are used to seeing psychic paper, and know what it looks like, such as Rose Tyler. (DW: The Empty Child)
 * Torchwood One personnel, due to psychic training. (DW: Army of Ghosts)
 * William Shakespeare, apparently due to his incredible mind. (DW: The Shakespeare Code)
 * Ernest Shackleton, likely due to the explorer's driven and determined nature. (DWM: The First)
 * Eve (NSA: The Last Dodo)
 * Morret and other veterans of the Telepath Uprising. (NSA: Judgement of the Judoon)
 * GateBots (DWM: Attack of the GateBots!)
 * Rosanna Calvierri (DW: The Vampires of Venice)
 * Frederick Abberline (IDW: Ripper's Curse)
 * The Anglican Marines of the Church, who trained themselves for the battle of Demons Run. (DW: A Good Man Goes to War)

Related items

 * Psychic credit card
 * Suggestibility paper