Hologram

Holograms were projections of light by a laser beam (TV: The Talons of Weng-Chiang) which cast three-dimensional images used for information storage and communication. Some holograms were also capable of developing sentience or being used to recreate life.

Variations
Holograms were usually projected from a device, meaning that they were generally stationary. Some were mobile, however, and appeared not to be connected to a projector, at least not visibly.

A type of holograms, hologlyphs, could materialise and dematerialise at will or when summoned, could be programmed not to know they weren't real, and could have a solid feel to them as if they were real beings. A hologlyph of a recently deceased person could even be created to acquire as to the last few moments of their life. They were also able to interact with machinery, as Book was able to connect with the lexicon. (AUDIO: ...ish)

Xanxia was able to create a permanent cellular regeneration projection of herself, always nearly complete but forever connected to the real Xanxia whose near-dead body was preserved between two time dams. The Doctor could not switch her off, and was even slapped by her. She could also physically interact with her surroundings and her personal devices, which might have been projected as well, were also physical. (TV: The Pirate Planet)

Distant past
150 million years BC, the Kastrians had a hologram recorded to tell Eldrad aeons later that his mission to revive the race had failed. (TV: The Hand of Fear)

19th century
In 1890s London, the 51st century Magnus Greel employed the holographic technique to pretend the presence of a ghost guarding his lair under the Palace Theatre. (TV: The Talons of Weng-Chiang)

20th century
In 1938, with little time left, the Eleventh Doctor used the TARDIS' voice interface, which variously took on the images of Rose Tyler, Martha Jones, Donna Noble and Amelia Pond. (TV: Let's Kill Hitler)

In 1969, the Eleventh Doctor showed Canton Delaware a holographic projection of a Silent. (TV: Day of the Moon)

21st century
In 2007, when Sally Sparrow inserted a DVD with the Tenth Doctor's message to her into the TARDIS console, it opened a projection of the Doctor, who announced the TARDIS was returning to his timestream. (TV: Blink)

In 2008, the Eleventh Doctor called the Atraxi back to check if Earth violated their laws, and if it was defended, which the Atraxi confirmed with holograms. The holograms showed Pete's World Cybermen, Daleks flying out of the Genesis Ark, Dalek Sec, a Sea Devil, a Reaper, a Sontaran, the Empress of the Racnoss, Vashta Nerada operating a spacesuit, Hath, Ood and a Sycorax for those who had attacked Earth in the past. For its protector, it showed the first, second, third, fourth, fifth, sixth, seventh, eighth, ninth, and tenth incarnations of the Doctor. (TV: The Eleventh Hour)

Captain John Hart used his vortex manipulator to send holographic messages to Captain Jack Harkness and the rest of Torchwood Three. (TV: Kiss Kiss, Bang Bang, Fragments)

Captain John projected an image to Torchwood of a canister containing what he thought was part of a key to find an Arcadian diamond, but were actually parts to a bomb that attached to the DNA of whoever killed the woman that owned this canister. When Captain John, the woman's murderer, assembled these pieces, it projected a hologram recording of this woman to tell him this. (TV: Kiss Kiss, Bang Bang)

In 2009, the Shadow Proclamation used holograms to show the 27 planets the Daleks had stolen. (TV: The Stolen Earth)

In 2010, the Claw Shansheeth had an epitaph stone declaring the Eleventh Doctor's death, which Mr Smith projected as a hologram. (TV: Death of the Doctor)

In 2011, the Skullions under order of Harrison made and controlled a hologram of Joseph Serf during the release of the SerfBoard. This hologram had hypnotic powers that willed people to buy the SerfBoard. Luke and Sky Smith later took control, telling the journalists at the release that the SerfBoard was junk. (TV: The Man Who Never Was)

In 2050, Medes captured by Inspector Drake projected holograms to warn K9 and his gang about the chenium pollution Drake had caused. (TV: Alien Avatar)

23rd century
On 23rd century Deimos, holograms were recorded on cameras in a similar way to photographs. (AUDIO: Deimos)

44th century
In the 44th century, Amy Pond, as the Ghost of Christmas Present, showed Kazran Sardick the ship she was on that was about to crash into a planet through the use of holograms. (TV: A Christmas Carol)

61st century
In 6012, the humans and Hath on Messaline used holograms to show a map of their residence. (TV: The Doctor's Daughter)

Far future
The TARDIS projected a hologram of the Ninth Doctor saying goodbye to Rose Tyler, when he thought he had no way out from the Game Station in 200,100. (TV: The Parting of the Ways)

On 5,000,000,053 New Earth, Sally Calypso was a hologram newsreader. (TV: Gridlock)

Pete's World
The Tenth Doctor projected himself as a hologram into Dårlig Ulv Stranden on Pete's World while he said his final farewells to Rose Tyler from his own universe. (TV: Doomsday)

Unknown dates
A hologram of Mel Bush was created by the Rani to trick the Seventh Doctor into giving her back a component of her Time Manipulator. The hologram could move like her and disappeared when the Doctor tried to embrace her. (TV: Time and the Rani)