Time-Space Visualiser

A Time-Space Visualiser (also known as a Space-Time Visualiser or Time Television) was a device that allowed the operator to view any event in history.

History
The origins of the Visualisers remain unknown. One ended up in the Space Museum of the Morok Empire and was given to the First Doctor by Tor as a souvenir after helping to defeat the Moroks. (TV: The Space Museum)

After getting the Visualiser working, the Doctor and his companions used it to observe Queen Elizabeth I and Francis Bacon meeting with William Shakespeare, Abraham Lincoln delivering his Gettysburg Address and the Beatles performing "Ticket to Ride". The Visualiser later showed them the Daleks launching their time machine on a mission to exterminate them, which let them buy some time. (TV: The Chase)

The Third Doctor later used the Visualiser to trace the origin of an alien spaceship fragment to the island of Salutua in 1934, creating a time bridge to that year. (PROSE: The Eye of the Giant) He kept it as late as his eleventh incarnation where he used it to observe the timeline after he repaired the Daleks' alterations using the Eye of Time. (GAME: City of the Daleks)

The Sixth Doctor watched the 2006 cricket Test Match between Australia and South Africa shortly after defeating Davros and the Daleks at the Battle of Waterloo on 18 June 1815. Flip Jackson described it as a "manky old thing" and criticised it for being in black and white. (AUDIO: The Fourth Wall)

While his granddaughter Susan Campbell and great-grandson Alex Campbell were celebrating Christmas in the TARDIS with him and Lucie Miller, the Eighth Doctor wanted to watch the Queen Elizabeth II's 1953 Christmas speech using the Visualiser as that was a "great year." (AUDIO: Relative Dimensions)

The Sixth Doctor once told Evelyn Smythe that the Time Lords had Time-Space Visualisers which they used to spy on him. (AUDIO: The 100 Days of the Doctor)

The Daleks used a similar device, the Visualiser, which Amy Pond called a 'Librarian Dalek'. (GAME: City of the Daleks)

Functions
The Visualiser could "tune in" to events all over the universe in many time eras. The First Doctor said that the Visualiser could only show events in the past. (TV: The Chase) However, Faction Paradox used a Time-Space Visualiser (presumably a different model) to forecast Fitz Kreiner's future, showing him an image of himself as Father Kreiner. (PROSE: The Ancestor Cell) Izzy Sinclair used the Time-Space Visualiser to play various video games, such as Happy Deathday, which involved the Eighth Doctor and his past incarnations. (COMIC: Happy Deathday)

Behind the scenes

 * The New Zealand Doctor Who Fan Club has a long-running fanzine called Time-Space Visualiser or TSV for short.