In Greek myth, Pegasus was born from the blood of the head of Medusa (a monster who turned men to stone) when she was killed. Nobody could tame this magical flying horse until Bellerophon, a warrior in exile from Corinth, was helped by the goddess Athene. She gave him a magic bridle with which he managed to subdue Pegasus. They had several adventures together; in the most famous story, Pegasus helped Bellerophon to overcome the Chimaera, a monster made from the parts of different beasts (rather like the Sphinx.) It was also said that Bellerophon defeated the all-female Amazon tribe in battle.
In the end, however, Bellerophon went too far and tried to fly up to Mount Olympus (home of the gods) riding on Pegasus. The chief god Zeus instructed Pegasus to throw him off, and Bellerophon was crippled by the fall. There is a constellation called Pegasus, named after the myth.