When a group of insectile scientists discovered a crystal palace outside of time called the Panoptichron, they accidentally damaged time itself by manipulating the palace's systems. To redeem themselves, these "Timebreakers" gathered teams of agents from across the multiverse to visit alternate realities and repair broken chains of events caused by their actions, "healing" the timelines by putting them back on their proper path.
Using an interactive avatar dubbed the Time Broker, the bugs convinced their agents they had each become "unstuck in time", and by fixing other realities they could create a domino effect that would restore their individual place in the timestream. Each team was given a Tallus, a device which informed them of their mission in each reality, and governed their jumps between worlds.
The Exiles were one such team, appearing in their own series from Exiles (1st series) #1-100, New Exiles #1-18, and Exiles (2nd series) #1-6. For the first 66 issues, the Exiles operated under a strict "one in, one out" policy, with a new member materializing to replace one who died or was incapacitated. At that point, however, the Exiles made their way to the Crystal Palace and took control of the Timebreakers' system, giving them more control over their membership and travels.