In the aftermath of the events of Second Coming, Cyclops felt there was no longer a need for his wet works teams, X-Force. However, Wolverine and Archangel had other ideas. They both felt that there still needed to be a team dedicated to those sorts of job and along with Psylocke, Fantomex, and Deadpool they reformed a new team.
Feeling that the team would need separate space away from Utopia, Archangel (using his fortune as Warren Worthington III) built a state of the art Cavern-X. The complex includes both living and training quarters.
Much like the Batcave, this cavern contains homages to the X-Men's past. In case of mutants getting wiped out there were mementos of the teams history such as pictures of the Original X-men and Giant Sized teams, members former costumes (Storm and Havok former costumes are seen as well as Magneto's helmet and Sunfire's mask). There are also reminders of major enemies like a giant sentinel head and a large Brood sculpture. Archangel said this was for future generations to know about the X-men.