The JLA's first trip to the universe is where Owlman is found hacking computer systems to get the info he needs. There, the JLA fights recruits the Crime Syndicate of America has recruited. Their second trip was when Batman followed Superwoman, and defeats her. After taking out Superwoman, he calls the JLA, and alongside the JLA travels to the moon, to get to the Crime Syndicate's headquarters. From there on, every JLA'er fights against their counterparts, and Wonder Woman manages to even win against her counterpart, Superwoman.
Wonder Woman had a minor role in Young Justice. Initially, the character was going to be excluded from the show due to legal red tape, but was included at the last minute. However, as a result of only being cleared for use late in the production cycle, she only had several speaking appearances. In the second season, she could be seen as the mentor of Wonder Girl. She was voiced by Maggie Q.