In Greek mythology, Styx ("[river of] hate") is the name of a river which formed the boundary between earth and the underworld, Hades. It circles Hades nine times. Styx and Phlegethon, Acheron and Cocytus converge on the center of the Hades on a great marsh. Other important rivers of Hades are Lethe and Eridanus.
Styx is guarded by Phlegyas, who passes the souls from one side to another of the river. In other versions, Phlegyas guards Phlegethon, another of the main rivers of Hades, but Dante put Phlegyas over the Stix.
The gods respected the Styx and swore binding oaths by it. Zeus swore to give Alcmene whatever she wanted and was then obliged to follow through, resulting in her death. Helios similarly promised Phaeton whatever he desired, also resulting in his death. Gods that did not follow through on such an oath had to drink from the river, causing them to lose their voices for nine years.
Styx was primarily a feature in the afterworld of Greek mythology, but has been described as a feature present in the hell of Christianity as well, notably in the Divine Comedy. The ferryman Charon is in modern times commonly believed to have transported the souls of the newly dead across this river into the underworld, though in actuality it was the river Acheron that Charon plied.
Styx is also the name of a primordial goddess who represented that river. She was a daughter of Erebus and Nyx. With Pallas, she was the mother of Zelus, Nike, Cratos and Bia (and sometimes Eos).