In Greek mythology, Styx (/ˈstɪks/ ^ⓘ; Ancient Greek: Στύξ [stýks]; lit. "Shuddering"), also called the River Styx, is a goddess and one of the rivers of the Greek Underworld. Her parents were the Titans Oceanus and Tethys, and she was the wife of the Titan Pallas and the mother of Zelus, Nike, Kratos, and Bia. She sided with Zeus in his war against the Titans, and because of this, to honor her, Zeus decreed that the solemn oaths of the gods be sworn by the water of Styx.

According to the usual account, Styx was the eldest of the Oceanids, the many daughters of the Titan Oceanus, the great world-encircling river, and his sister-wife, the Titaness Tethys. However, according to the Roman mythographer Hyginus, she was the daughter of Nox ("Night", the Roman equivalent of Nyx) and Erebus (Darkness).

She married the Titan Pallas and by him gave birth to the personifications Zelus (Glory, Emulation), Nike (Victory), Kratos (Strength, Dominion), and Bia (Force, Violence). The geographer Pausanias tells us that, according to Epimenides of Crete, Styx was the mother of the monster Echidna, by an otherwise unknown Perias.

Although usually Demeter was the mother, by Zeus, of the underworld-goddess Persephone, according to the mythographer Apollodorus, it was Styx. However, when Apollodorus relates the famous story of the abduction of Persephone, and the search for her by her angry and distraught mother, as usual, it is Demeter who conducts the search.

Styx was the oath of the gods. Homer calls Styx the "dread river of oath". In both the Iliad and the Odyssey, it is said that swearing by the water of Styx is "the greatest and most dread oath for the blessed gods". Homer has Hera (in the Iliad) say this when she swears by Styx to Zeus, that she is not to blame for Poseidon's intervention on the side of the Greeks in the Trojan War, and he has Calypso (in the Odyssey) use the same words when she swears by Styx to Odysseus that she will cease to plot against him. Also Hypnos (in the Iliad) makes Hera swear to him "by the inviolable water of Styx".

Examples of oaths sworn by Styx also occur in the Homeric Hymns. Demeter asks the "implacable" water of Styx to be her witness, as she swears to Metaneira, Leto swears to the personified Delos by the water of Styx, calling it the "most powerful and dreadful oath that the blessed gods can swear", while Apollo asks Hermes to swear to him on the "dread" water of Styx.

Hesiod, in the Theogony, gives an account of how this role for Styx came about. He says that, during the Titanomachy, the great war of Zeus and his fellow Olympians against Cronus and his fellow Titans, Zeus summoned "all the deathless gods to great Olympus" and promised, to whosoever would join him against the Titans, that he would preserve whatever rights and offices each had, or if they had none under Cronus, they would be given both under his rule. Styx, upon the advice of her father Oceanus, was the first to side with Zeus, bringing her children by Pallas along with her. And so in return Zeus appointed Styx to be "the great oath of the gods, and her children to live with him always."

According to Hesiod, Styx lived at the entrance to Hades, in a cave "propped up to heaven all round with silver pillars". Hesiod also tells us that Zeus would send Iris, the messenger of the gods, to fetch the "famous cold water" of Styx for the gods to swear by, and describes the punishments which would follow the breaking of such an oath: