Polyphemus was born to Poseidon, the god who shakes the earth and rules the wide sea, and Thoosa, a daughter of Phorcys, the ancient sea-god whose brood includes the Gorgons and the Graeae, the three grey sisters who share a single eye and a single tooth. He was a Cyclops, one of the one-eyed giants who dwell in the far west, and he made his home on the island of Sicily near the smoking peak of Mount Etna, the volcano whose fire the Greeks believed was the forge of Hephaestus, the lame smith-god. The Cyclopes were a race without law or agriculture, trusting in the gods and tending their flocks in solitary caves. Polyphemus kept sheep and goats by the hundred, milking the ewes into wicker pails and curdling the milk into cheese that he stacked on racks inside his cavern. He had no wife, no companions, and no fear of strangers, for he believed himself invincible behind his stone door.

The defining episode of his life came when Odysseus, the king of Ithaca who had spent ten years fighting at Troy and was now struggling to reach home, landed on Sicily with twelve of his crew. They found a cave stocked with cheese and milk pails, and the hungry men helped themselves while waiting for the owner to return. At evening, Polyphemus drove his flocks inside, rolling a boulder across the entrance that no force of mortal men could move. When he saw the intruders, he did not ask their business but seized two of them, dashed their brains out against the stone floor, and devoured them raw, tearing limb from joint and drinking their blood. The survivors cowered in the shadows while the giant finished his meal and lay down to sleep among his sheep.

Odysseus knew that brute force could not prevail against a creature who moved mountains for door-stops, so he turned to cunning. The next evening, after Polyphemus had eaten two more men, Odysseus offered him a skin of strong wine that he had brought from Ismarus, a gift meant to soften the giant's heart. Polyphemus drank it down and asked for more, then demanded to know the stranger's name. Odysseus replied that he was called Outis, which means Nobody in Greek, and the drunken giant promised to eat Nobody last as a mark of favour. When the wine had done its work and Polyphemus lay snoring, Odysseus and his remaining men heated a wooden stake in the fire, sharpened it to a point, and drove it into the giant's single eye with all their strength. The stake hissed and sizzled in the socket, and Polyphemus roared so loudly that the cavern shook and the other Cyclopes came running from their caves on the mountainside. He bellowed that Nobody was killing him, and because he used that name, they told him that if nobody was attacking him, he must be ill, and they went away.

The next morning, Odysseus tied his men beneath the bellies of the sheep and clung to the fleece of the largest ram himself, so that when the blinded giant felt the backs of his flock as they left the cave, he found only wool and let them pass. Once outside, Odysseus could not resist revealing his true name, and Polyphemus cried out to his father Poseidon to curse the man who had blinded him. The sea-god heard his son's prayer and unleashed storms and contrary winds that would drive Odysseus across ten more years of wandering before he ever saw Ithaca again.

In later years, another story grew up around Polyphemus. The giant fell in love with Galatea, a sea-nymph of such beauty that she shone like foam upon the waves, but she scorned his clumsy advances and loved instead Acis, a handsome Sicilian youth descended from the river-god Faunus. Polyphemus sang love-songs to Galatea from the shore, comparing her to cheese and milking-pails in verses that the poets found both comic and pitiful, but she fled from him into the sea. In a fit of jealous rage, the giant tore a boulder from the mountainside and hurled it at the lovers. The rock crushed Acis, and Galatea wept so bitterly that the gods took pity and transformed the dying youth into a river, the Acis, which still flows on Sicily. Polyphemus was left alone on his mountain, blind in one eye and empty in his heart, a monster who wanted love and found only stone.