Originally the Institute was an alliance of some of the greatest foes of the Squadron Supreme joined together by the Scarlet Centurion to combat the Squadron in a battle arranged as a contest between the Centurion and the Grandmaster. Losing the battle the Institute were incarcerated but eventually escaped.
After the Squadron began their Utopia Program the Institute went into hiding. The Golden Archer was expelled from the Squadron and was captured shortly thereafter by the Institute. He was tortured and interrogated by the Institute who gained information about Tom Thumb's behavior modification machines as well as the locations of the Squadron members families. Ape-X (leader of the Institute) sent Lamprey after Arcanna Jones's husband and children, Foxfire was sent after Power Princess's husband, Quagmire went to retrieve the wife and children of the Whizzer, and Doctor Decibel and Shape were sent after the mother of the Blue Eagle.
After the kidnappings, the Institute (except Ape-X) attacked Tom Thumb at Squadron headquarters, behavior modifying Tom to obey their commands and setting up an ambush for the rest of the Squadron. The Squadron surrendered once the Institute revealed they held the Golden Archer and their family members captive. The Whizzer, who was the last to arrive, escaped while the other members were behavior modified similar to Tom Thumb. Eventually Whizzer was captured as well and all of the Squadron members were brought to the Institute’s base where the hostages were being held. Upon arrival at the Institute’s headquarters the Squadron attacked the Institute’s members and rescued the hostages, revealing that Tom Thumb had adjusted the behavior modification machines so that they wouldn’t work on Squadron members.
Once the Institute of Evil members were defeated they were behavior modified to be contributing members of society and later were voted into the Squadron completely disbanding the Institute.