Time-Space Visualiser
A Time-Space Visualiser (also known as a Space-Time Visualiser) was a device that allowed the operator to tune in to any event in history.
History
The Doctor was given a Time-Space Visualiser by Tor as a souvenir. (DW: The Space Museum) After getting it working again, the Doctor and his companions used it to observe Queen Elizabeth I and Francis Bacon meet with William Shakespeare, Abraham Lincoln deliver his Gettysburg Address, and The Beatles perform "Ticket to Ride". The Visualiser later showed them the Daleks launching their time machine on their mission to exterminate them. (DW: The Chase)
The Doctor later used his Visualiser to trace the origin of an alien spaceship fragment to the island of Saluta in 1934, creating a time bridge to that year. (MA: The Eye of the Giant) He kept on to his as late as his eighth incarnation (DWM: Happy Deathday)
Functions
The Visualizer could "tune in" to events all over the universe in many time eras. The Doctor said that the Visualizer could only show events in the past. (DW: 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. (EDA: The Ancestor Cell) Izzy Sinclair used the Time-Space Visualiser to play a video games involving the Doctor and his past incarnations. (DWM: Happy Deathday)
Behind the Scenes
The New Zealand Doctor Who Fan Club has a long-running fanzine called Time-Space Visualizer, or TSV for short.