Infinity Island is a sovereign island located somewhere in the Caribbean Sea. It is home to Ra's al Ghul and his family, and the former headquarters of the League of Shadows. Ra's has a vast fortress complex on the island, with modern security and numerous guards. It also has a Lazarus Pit.
After being killed on a mission at Cape Canaveral, Ra's al Ghul's body was revived in the Lazarus Pit. Moments after he left, Hagen rose from the pit, and attacked them until he was put into an inert state by Ra's.
Brion Markov, Halo, Forager and Sphere infiltrated the island, believing the Shadows had Brion's sister. They were quickly dispatched and imprisoned by Sensei. They were soon rescued by Nightwing and others. a brief battle ensued as they attempted to escape, before Ra's al Ghul stopped it, informed the heroes that Tara was not there and that he was no longer part of the Light or Shadows, and let them leave.
Cheshire snuck onto the island seeking to end the contract on her life, one way or another. She was easily taken down by Sensei, who questioned why she would make such a foolish move. Cheshire argued with Talia al Ghul, until she received an emergency alert and fled.
Cheshire returned to confront Sensei again, seemingly on a suicide mission. Tigress intervened, and Cheshire admitted she was running from her family because she felt she was too much like her father and did not want her daughter to grow up like her. Sensei admitted that he had created a sense of family among the Shadows to manipulate people like Cheshire and Onyx into loyalty. Now that they were no longer part of the Shadows, Sensei and Ra's al Ghul offered Cheshire and Onyx the chance to stay there and work through their experiences with the Shadows, which both accepted.