In "The Doll House" story arch, he deserted the Dreaming and went to the waking world. He decided to become a serial killer that had a taste for eyes, but this was not what Sandman wanted (he wanted the Corinthian to show humanity it's own dark nature). After 40 years, Sandman destroyed him. In "The Kindly Ones", Dream created a new Corinthian with some of the memories of the previous one. He was sent to find and protect Daniel, where he battled Loki and Puck and ate their eyes.
The Sandman Presents: The Corinthian
This 3-issue mini-series we learn how the Corinthian I entered the waking world and learned to kill people. Here he displayed the ability to possess people.
In The Dreaming spin off, the Corinthian II returns to Earth in the "Souvenirs" story arch. He later hunts down Echo, but accidentally killed Matthew. So, he punished with becoming human and begins to understand human nature better and then is let back in the Dreaming.
Despite the fact he lacks eyes and has mouths instead, he doesn't appear to have any trouble with sight. When he eats people's eye, he can see what happen in their life. He can possess people, but his victim 's eye are replaced with mouths and gain white hair. The second Corinthian is skilled at hand-to-hand combat. He was seen snapping the neck of a supernatural wolf with out much effort. He is also resistant to damage and is fearless.
In "The Kindly Ones", Puck refused to tell Corinthian if his name is derived from "the letters, the pillars, the leather, the place, or the mode of behavior." This is likely a reference to the Letter to the Corinthians (which has phrase "Dark Mirror", which Dream use to describe the Corinthain), Corinthian style of pillars, Corinthian leather and Corinthian behavior (" indulging in luxury and licentiousness"). Neil Gaiman (the writer of The Sandman) revealed the name came from the mode of behavior.
The Sandman: The Doll House and The Kindly Ones