Polyphemus is a Cyclops, a giant shepherd with a single eye, son of Poseidon, who lives in a cave with his flocks. The Cyclopes, Odysseus says, have no assemblies or laws: each one dictates the law to his children and wives and cares nothing for the others. Odysseus arrives at the cave with twelve companions, and Polyphemus traps them there, blocks the entrance with a stone they cannot move, and devours six of them, two at a time.
Odysseus could kill the Cyclops while he sleeps, but he realizes that if he did, they would die too, because no one else can push the stone. So he devises a plan: he offers Polyphemus strong wine, and the Cyclops asks the visitor's name, promising a guest gift. Odysseus replies: "Nobody is my name." The gift is the worst possible: "I will eat Nobody last." When the Cyclops sleeps, they heat an olive stake and drive it into his eye.
The other Cyclopes hear the cries and ask whether someone is harming him by force. Polyphemus answers: "Nobody is killing me by guile, not by violence." The neighbors conclude that he suffers from an affliction sent by Zeus and leave. Odysseus and the companions escape clinging to the bellies of the sheep, and his heart "laughed" to see how the name deceived the Cyclopes.
The trick has a cost. Already aboard the ship, Odysseus cannot resist the wish to be recognized and shouts his true name: "Odysseus, sacker of cities, son of Laertes, who has a house in Ithaca." Polyphemus prays to Poseidon, and it is this prayer that causes the pursuit that runs through the rest of the poem. For this reason the scene is read in two ways: as the triumph of cunning, in which a man without a name defeats brute force, and as the first example of a desire to be recognized that prolongs his suffering and that of his companions.