The Great Escape story arc which spanned over 20 issues and wasn't resolved until several issues into the relaunch of Thunderbolts as Dark Avengers. The Great Escape spun out of the events of Fear Itself and is easily broken up into several shorter chapters (mostly corresponding to the team travelling to a different time period or reality) and it all culminated in The Cataclysm.
The story sees members of the Thunderbolts (Boomerang, Centurius, Fixer, Man-Thing, Moonstone, Mr. Hyde, Satana, Troll) attempting to escape from the Thunderbolts program and winding up travelling through different periods of time and visiting future realities. The Thunderbolts remaining in the modern day (Ghost, John Walker, Juggernaut, Luke Cage, MACH-V, Songbird) begin a search for the escapees and are later joined by a new team of Thunderbolts comprised of members of the Dark Avengers (Ai Apaec, Ragnarok, Toxic Doxie, Trickshot) as well as help from Hank Pym and Skaar.
Time periods and realities visited included: World War II, Victorian London, Medieval times, sometime circa Thunderbolts #1, the day the Celestials first arrived on Earth, during the Masters of Doom storyline, the apparent end of the world, and finally a dystopian future policed by Luke Cage's grandson. For each reality, the team adopted new costumes to fit in with their surroundings and generally failed at their attempts to not alter history.
The ongoing story arc was met with mixed reaction by fans and didn't particularly help Thunderbolts which was already one of Marvel's lowest sellers. This led to the title being cancelled and replaced with Dark Avengers , despite it still continuing the story from Thunderbolts, which made the relaunch completely useless. Dark Avengers was eventually cancelled and the Thunderbolts broke up. Marvel decided to start from scratch and create a completely new revamped Thunderbolts team that has nothing in common with any of the previous iterations and instead stars some of their popular characters. None of the characters or themes from the previous Thunderbolts remain at all and several have been killed off, shunted to comic book limbo, or their development in Thunderbolts has been ignored.