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 hologram, 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 Fourth 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)

Another type, those made of hard-light, were used on the Orient Express to deceive passengers into believing the train was normal, creating hologram furniture and people. (TV: Mummy on the Orient Express)

A quantagram was a physical hologram, described by the Eighth Doctor as "real but not real", like stage sets in a theatre. They acted like real objects. (AUDIO: The Scapegoat)

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)

9th century
In the 9th century, the leader of the Mire used a hologram to disguise himself as the Viking god Odin. Later, Ashildr, using a Mire helmet, projected a holographic sea snake over a wooden puppet. (TV: The Girl Who Died)

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 Everett Delaware III a holographic projection of a Silent. (TV: Day of the Moon)

21st century
By the early 21st century, televisions were capable of holographic broadcasting. (PROSE: Cat's Cradle: Warhead)

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' vortex manipulator. (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 the 2010s, virtual reality conference calls made use of holograms. (AUDIO: In Memory Alone) UNIT used holograms of Silents in order to retain memories, and to manipulate others into following demands when necessary. (AUDIO: Silent Majority, In Memory Alone)

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)

22nd century
By the 22nd century, holographic slides had replaced paper as a writing medium. (PROSE: Fear Itself)

In 2119, the Twelfth Doctor projected a hologram ghost version of himself into the future. (TV: Under the Lake / Before the Flood)

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

24th century
In a parallel universe in the 24th century, Starfleet ships such as the USS Enterprise (NCC-1701-D) used a form of holographic technology called holodecks. (COMIC: Assimilation²)

Earth Empire
By the age of the Earth Empire, magazines had been abandoned in favour of holo-zines. (COMIC: Pirates of Vourakis)

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)

54th century
The TARDIS projected a pair of hologram antlers on the Twelfth Doctor's head at Christmas on Mendorax Dellora. (TV: The Husbands of River Song)

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)

The Cybermen made use of holo-transmissions during the Cyber-Wars of the "very far future" as their Cyber-ships were capable of both sending and receiving them. Aboard a stolen Cyberfighter, the Thirteenth Doctor received a holo-transmission from the partially converted Ashad. (TV: Ascension of the Cybermen) Aboard a Cybercarrier, Ashad himself received a holo-transmission from, speaking from the Capitol on Gallifrey. (TV: The Timeless Children)

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 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)

A Mondasian colony ship used holographic technology, as pointed out by. The solar farm possessed a hologram sky which provided a "bit of atmosphere". Even the lift shafts were holographic, so as to preserve the forest. (TV: The Doctor Falls)

Shortly following her regeneration, the Thirteenth Doctor claimed to have spent thirteen weeks as a hologram. (TV: The Ghost Monument)

Other references
Finding an 18th century French mantle aboard the SS Madame de Pompadour, the Tenth Doctor observed that it was not a hologram. (TV: The Girl in the Fireplace)

The Twelfth Doctor observed to Clara Oswald that the ghosts, later determined to have been created by the Fisher King, (TV: Before the Flood) were not holograms. (TV: Under the Lake)