In Greek mythology, Styx (/ˈstɪks/; Ancient Greek: Στύξ [stýks][citation needed]) is a deity and a river that forms the boundary between Earth and the Underworld, often called "Hades", which is also the name of its ruler. The rivers Styx, Phlegethon, Acheron, Lethe, and Cocytus all converge at the center of the underworld on a great marsh, which sometimes is also called the Styx. According to Herodotus, the river Styx originates near Feneos.[1] Styx is also a goddess with prehistoric roots in Greek mythology as a daughter of Tethys, after whom the river is named and because of whom it had miraculous powers.

The deities of the Greek pantheon swore all their oaths upon the river Styx because, according to classical mythology, during the Titan war, Styx, the goddess of the river, sided with Zeus. After the war, Zeus declared that every oath must be sworn upon her.[2] Zeus swore to give Semele whatever she wanted and was then obliged to follow through when he realized to his horror that her request would lead to her death. Helios similarly promised his son Phaëton whatever he desired, also resulting in the boy's death. Myths related to such early deities did not survive long enough to be included in historic records, but tantalizing references exist among those that have been discovered.

According to some versions, Styx had miraculous powers and could make someone invulnerable. According to one tradition, Achilles was dipped in the waters of the river by his mother during his childhood, acquiring invulnerability, with exception of his heel, by which his mother held him. The only spot where Achilles was vulnerable was therefore that heel, where he was struck and killed by Paris's arrow during the Trojan War. This is the source of the expression Achilles' heel, a metaphor for a vulnerable spot.

Styx was primarily a feature in the afterworld of classical Greek mythology, similar to the Christian area of Hell in texts such as The Divine Comedy and Paradise Lost. The ferryman Charon often is described as having transported the souls of the newly dead across this river into the underworld. Dante put Phlegyas as ferryman over the Styx and made it the fifth circle of Hell, where the wrathful and sullen are punished by being drowned in the muddy waters for eternity, with the wrathful fighting each other.

In ancient times some believed that a coin (Charon's obol) placed in the mouth of a dead person[3] would pay the toll for the ferry across the river to the entrance of the underworld. It was said that if someone could not pay the fee, they would never be able to cross the river. The ritual was performed by the relatives of the dead.

The variant spelling Stix was sometimes used in translations of Classical Greek before the 20th century.[4] By metonymy, the adjective stygian (/ˈstɪdʒiən/) came to refer to anything dark, dismal, and murky.