What is the 'Vortex Manipulator,' and how is it used in the show?

The 'Vortex Manipulator' is a wrist-mounted time travel device in the British television series 'Doctor Who'. It's a compact, portable and more primitive version of the TARDIS time machine, typically used by individuals or groups without a TARDIS of their own.

The device can transport the wearer through time and space, but only for relatively short distances. It has limited accuracy and can't transport the user to specific coordinates or moments in time, unlike the TARDIS. It's also not a safe way to travel as it can cause severe injury, disorientation or even death if used improperly or excessively.

In the show, the Vortex Manipulator has been used by various characters, both as a time travel device and as a way to communicate over time and space. It's been used by Captain Jack Harkness, River Song, and the Doctor himself on occasion, among others.