According to Hesiod and Apollodorus, Stheno and Euryale, along with Medusa, were daughters of the primordial sea-god Phorcys and the sea-monster Ceto. In this genealogy the three Gorgons belong to the family of monstrous sea-children descended from Phorcys and Ceto.

Hyginus, however, gives a different account: in his version the Gorgons were daughters of "the Gorgon" — described as an offspring of Typhon and Echidna — together with Ceto. The two traditions thus disagree on the Gorgons' paternity.

The Gorgons Stheno and Euryale were immortal, whereas their sister Medusa was mortal. The only story in which the two immortal sisters take part is their pursuit of Perseus after he had beheaded Medusa.

The Shield of Heracles describes the chase, with the Gorgons rushing after Perseus, dreadful and unspeakable, serpents at their girdles and snakes writhing in their hair. Because Perseus beheaded Medusa by looking at her reflection and then fled wearing the cap of Hades, which made him invisible, Stheno and Euryale chased after him but could not see him and so failed to catch him.

Euryale's cry during the pursuit is remembered in later poetry. Pindar relates that Athena invented the music of the flute (the aulos) in imitation of the shrill lament of Euryale, while Nonnus describes Perseus listening for no trumpet but Euryale's bellowing.

In archaic art (roughly the eighth to fifth centuries BC) the Gorgons are typically shown with the head turned frontally to face the viewer, set — seemingly without a neck — atop a running body shown in profile, with wings on the back and curl-topped boots. Notable examples include the work of the Gorgon Painter and various ancient vases.

In later depictions the Gorgons appear with proportionally smaller heads, visible necks, and a generally less wild and monstrous appearance, reflecting a gradual softening of the type over time.