The Teselecta, designated Justice Department Vehicle Number 6018, was a humanoid starship/time machine, similar to an android, staffed by a crew who had been miniaturised by a compression field. It was used to locate people deemed guilty of crimes who had escaped punishment. After finding them near the end of their respective timelines to avoid changing history, the crew would administer their own punishment, usually in the form of some non-lethal, painful torture. Afterwards they could die in the manner recorded by history.
The Teselecta had a crew of 421 people led by Captain Carter. They could change its appearance to that of any humanoid being. When the Eleventh Doctor, Amy, Rory and Mels crashed the TARDIS into Adolf Hitler's office, the Teselecta was trying to punish Hitler, but got him too early. When they saw Mels, who had regenerated, they recognised her as Melody Pond and stopped their pursuit of Hitler to punish her instead; their records showed she would kill the Doctor. They were thwarted by her parents, who turned off the devices protecting the crew from the ship's antibodies. They teleported to a spaceship above the Earth, abandoning the Teselecta, which was used to show Melody that she would become River Song, a good friend of the Doctor and one of his companions. This helped Melody to resist her childhood programming as the Silence's assassin. The Doctor also had it reveal the Silence's purpose and extracted data from it regarding his death. (TV: Let's Kill Hitler)
The Teselecta was later recovered by its crew. They investigated the Silence by posing as Gideon Vandaleur, a deceased envoy of that cult. The Doctor approached the Teselecta for information. After sending the Doctor to someone who could help, the Teselecta was again approached to deliver the Doctor's mail lest he cross his own timestream. The Captain asked the Doctor if there was anything else they could do, as they really did believe in justice and wanted to help, despite the Doctor's contempt. The Doctor asked for the Teselecta to pose as him and fake his death. (TV: The Wedding of River Song)
In the main timeline, River Song "killed" the Teselecta, in the guise of the Doctor, and it was destroyed when "the Doctor's body" was burned on a funeral pyre, with its passengers having evacuated before this. (TV: The Impossible Astronaut) In another, she prevented the Doctor's "death". This created an alternate universe in which, now that a fixed point in time had changed, time was breaking down. It found this world's versions of Amy and Rory and went to Area 52 with them.
The Doctor, inside the Teselecta, married River. He revealed himself to her. When River and the Teselecta touched, the timeline restored itself and Time continued on its wonted course. (TV: The Wedding of River Song)
The Teselecta could resemble anyone or anything whose likeness it has scanned. During its time in Berlin, 1938, it took on the forms of a cleaner, a Nazi official, a Nazi soldier (with and without a motorbike), as well as Amy Pond and River Song. A member of the crew said it had once taken the form of Rasputin, but with green skin. (TV: Let's Kill Hitler) At some time in the future the Teselecta took the form of Father Gideon Vandaleur, a deceased member of the Silence and at his request on 22 April 2011, the Eleventh Doctor. (TV: The Wedding of River Song) It was able to mimic regeneration at Lake Silencio. (TV: The Impossible Astronaut) The Teselecta had a lot of damage resistance, as the Doctor declared that he "barely got singed" when his 'body' was being cremated at Lake Silencio. (TV: The Wedding of River Song)
The Teselecta was equipped with a miniaturisation ray, which it used to shrink people and transport them into the Teselecta. Compression fields were used to keep people miniaturised.