According to the Odyssey, Odysseus arrived at the island of the Cyclops (Sicily), while trying to go back to his homeland, Ithaca. There, he and his men went into a cave that was full of food. Polyphemus, who dwelled in the cave, returned and sealed the entrance, so that none would escape; then he grabbed two of Odysseus' men and ate them. The next morning, he left to attend to his sheep, but not without eating two more of the men.
Upon his return, Odysseus offered him some strong wine he had with him, intoxicating him. Polyphemus, drunk, asked what the kind man's name was, and Odysseus replied "No one". Polyphemus said that he would eat "No one" last for gratitude, and fell into a deep sleep. Odysseus, having planned this, took a wooden stake and blinded Polyphemus' single eye. The giant started screaming for help, but when the other giants arrived, they told them "No one" had blinded him; his friends thought that a god had attacked him and told him to pray.
The next morning, Polyphemus took the sheep out of their pen to graze, and unable to see, felt each sheep's back in case the men were trying to escape. However, Odysseus had told his men to tie themselves under the animals. The men reached the ship, and when they set sail, Odysseus boasted to Polyphemus by revealing his name. Polyphemus then asked his father to punish Odysseus, causing him to deviate from his planned route even further.