In the motion picture Batman Begins (2005), the League was instead called the League of Shadows, and existed to fight what they perceived as injustice in the world. They trained Bruce Wayne for some years, until he could best any of the League in single combat, but he rejected them when the time came for him to kill a criminal, having realized that he must retain his compassion or he would become like the criminals he fought. The League's original base was destroyed in the subsequent battle as Bruce fought Ra's, but either enough men escaped the blaze or Ra's had other groups in the world, as they eventually attempted to strike at Gotham. Despite their best efforts, Bruce Wayne, now Batman, was able to fight off four members of the League single-handedly before challenging Ra's himself.
Dark Knight Rises
Bane, who had been exiled from the League by Ra's, took control of it and sought to fulfill al Ghul's final wish of destroying Gotham. He was in fact working for Talia, the daughter of Ra's.