Their first performances were in 1976 and their last gig was in San Francisco in 1981 (recorded and released as "Mission Of Dead Souls"),
Throbbing Gristle officially began at September 3, 1975 and they officially split on June 23, 1981. After they split, Genesis and Peter formed Psychic TV (and Peter later joining Coil) and Chris and Cosey becoming, well, Chris & Cosey. They came back together 23 years later in 2004 to plan an ill-fated weekend festival, which became a one-off recording session in London when the festival fell through, releasing a limited TGNOW album of the recordings.
A series of new releases and remasters followed as well as live performances. In 2010, Genesis withdrew from touring with TG and the three other members renamed themselves X-TG. However, Peter's death in November that year brought an end to TG/XTG for good. One final release, released under the name X-TG, followed in 2012.
A note on bootlegs: Throbbing Gristle was an organisation and all releases had to be approved by the organisation, not individual members. Most official releases were released by Industrial Records, Fetish Records and Mute (some exceptions exist).