In Greek mythology, Bellerophon was Pegasus' master. Bellerophon was the son or foster son of the sea god Glaucus, and Pegasus was a winged horse. Bellerophon captured Pegasus with a golden bridle given to him by the goddess Athena.
Bellerophon's relationship to Pegasus was a mixed blessing. One of the first things he did after taming the horse was to kill a man, though accidentally. Bellerophon was acquitted of this crime by King Proetus. Later, the king suspected Bellerophon of cuckolding him, though this wasn't true. Proetus sent Bellerophon to his father-in-law, Iobates. Bellerophon rode Pegasus to Iobates's palace.
When Iobates learned of Proetus' accusations against Bellerophon, he set Bellerophon to perform a series of tasks. These tasks would have been deadly for a man who didn't have Pegasus as his mount. Among the tasks were the killing of the Chimaera, the conquest of the Solymi and the conquest of the Amazons. Bellerophon, with Pegasus's help, even vanquished Iobates's own army. This convinced Iobates that Bellerophon was favored by the gods and innocent of Proetus' accusations.
All went well till Bellerophon decided to use Pegasus to fly to Mount Olympus. This offended Zeus, who sent a gadfly to torment Pegasus. The winged horse threw Bellerophon off. The fall crippled Bellerophon, and his hubris made him an outcast.