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. It was based on Venderman's Law. (PROSE: The Chase)

History
The origins of the Visualisers were unknown to the Doctor. 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 Visualiser had an instruction manual. (AUDIO: The Doctor's Tale)

The Third Doctor later used the Visualiser to trace the origin of an alien spaceship fragment to the island of Salutua in 1934. He used the same experiment to try and create a time bridge to that year in an attempt to bypass his exile, but this was only possible due to the unique nature of the omicron radiation contaminating the fragment. The time bridge project was abandoned after his trip to Salutua nearly had disastrous consequences for history. (PROSE: The Eye of the Giant)

With the Visualiser returned to its original purpose, the Doctor 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)

Shortly before arriving on Olleril, Bernice Summerfield watched something funny on the Visualiser. (PROSE: Prelude Tragedy Day)

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)

At the onset of the New Dalek Paradigm, the Strategist Dalek used a Time-Space Visualiser to observe the Dalek Empire's Robomen, ordering the Scientist Dalek to create the Dalek puppets based off their designs. (PROSE:  The Astounding Untold History of the Greatest Enemies of the Universe) They later developed their own version of the technology, the Visualiser, which Amy Pond called a "Librarian Dalek". (GAME: City of the Daleks)

Iris Wildthyme had a similar device, a time-space kinetograph. (PROSE: Beguine)

The Monk also had a Time-Space Visualiser. (AUDIO: The Resurrection of Mars)

Functions
The Visualiser could "tune in" to events all over the universe in many time eras. The First Doctor said that the Visualiser converted "neutrons of light energy into electrical impulses" and that it 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)