|Purpose||Returning to the past, erasing memories|
Team Lyoko usually activates a time reversion after an attack to make sure nobody remembers the events that transpired. People who have been materialized into the Supercomputer usually remember the events of the previous timeline, unless someone is possessed by X.A.N.A. (Odd in Killer Music and Attack of the Zombies). However time reversions cannot deactivate towers. (A Great Day)
In Amnesia it was shown that time reversions can and do regain the memories of people if they had been erased by an amnesia pandemic.
The return to the past program was rarely used after the episode A Great Day, when X.A.N.A. constantly rewinds the same Tuesday over and over, to increase his power, leaving the Lyoko Warriors in a cinch. Return to the past played a huge part in creating the Scyphozoa. Also, time reversions can be very dangerous, as Jeremy used it with the head set that multiplied his intellect by 10 every time he used it. It was apparently full of memory from Franz Hopper, Aelita's Father.
The characters in the show have used the time reversion to their own personal gain: Ulrich used it to win the lottery in a misguided attempt to prevent Yumi from moving back to Japan, which got him banished from the group temporarily (The Chips Are Down) and Franz Hopper used this feature 2546 times over the course of his research, becoming more and more mentally unstable with each time reversion.
Jeremie is usually the one that activates the time reversion process, though all the other members of the team are shown to be capable of activating it as well.
In the third season, most likely since X.A.N.A. had escaped from the supercomputer and didn't power up with it anymore, Jeremie seemed more relaxed about returning to the past even though sometimes it wasn't needed like in the first season.
During Code Lyoko Evolution it is revealed that Laura Gauthier modified the boundaries of the Return to the Past program during the episode Virus without Jeremie's knowledge to include herself to be unaffected by the memory loss side effect. This seems to be the only alternative to remember events after a time reversion which doesn't include the subject to be materialized into the Supercomputer. It was also revealed that Time Reversion can erase Lyoko Warriors memories as well, if they would be too much of an risk for other group. This was done by Jeremie to Laura, who lost completely every memory she had about Lyoko Warriors and their fight against X.A.N.A and professor Tyron.