In Odyssey Book 9 Odysseus and some of his men enter a cave stocked with provisions. Polyphemus returns with his flocks, blocks the entrance with a great stone, scorns xenia, and eats two men; he eats more the next day. Odysseus offers him strong undiluted wine; when the giant asks his name, the hero answers Οὖτις — "Nobody" — and Polyphemus promises to eat Nobody last.

While the Cyclops sleeps drunk, Odysseus and his men heat a sharpened stake and drive it into the single eye. When Polyphemus cries that Nobody is killing him, neighbouring Cyclopes assume divine affliction and leave. At dawn the blind shepherd feels the backs of his sheep as they go out; the men escape tied beneath the animals. As the ship pulls away Odysseus boastfully reveals his true name — hubris that lets Polyphemus pray Poseidon for revenge and hurl great rocks after them.

Euripides' satyr play Cyclops retells the episode with comic relief from a chorus of satyrs. His Polyphemus is more verbally sophisticated — a figure critics have compared to contemporary sophists — and the exchange of rhetoric turns hospitality into deadly barter. The play localises him on Mount Etna in Sicily and keeps Silenus and the satyrs as his slaves.

From Philoxenus of Cythera's dithyramb Cyclops or Galatea onward, classical poets linked Polyphemus with the sea-nymph Galatea. In that tradition he is often an unsuccessful rustic suitor, comic in his size and musical failings; later authors sometimes make him a successful lover and skilled musician. Ovid's Metamorphoses sets the Sicilian Cyclops crushing Galatea's mortal lover Acis with a thrown crag — the Odyssey's cannibal reborn as the volcano-dwelling rival after Troy.

The Galatea strand fed Renaissance and Baroque literature and opera (Góngora, Lully, Handel's Acis and Galatea, and many others), usually pastoral in tone and centred on the lovers while Polyphemus supplies comic or tragic rage.

The blinding and the escape under the sheep are among the earliest Odyssey scenes on seventh-century Greek vases; later Imperial sculpture (the Sperlonga group associated with Tiberius) restaged the blinding at life size. European painters from Jordaens to Turner favoured the escape, the rock-hurling giant, or the derisive departure of the ship.

Folktales of a clever hero who blinds a man-eating giant and escapes under animals are widespread across Eurasia; modern scholarship generally treats Homer as adapting older "Polyphemus legends" (ATU 1137) rather than inventing the type. This Homeric shepherd-giant remains distinct from Hesiod's Ouranian smith-Cyclopes who forge Zeus's thunderbolt.