Epic and classical Greek use Odys(s)eus; vase inscriptions preserve variants such as Oliseus, Olyseus, Olysseus, Olyteus and Ōlysseus. Magna Graecia attests Oulixēs; Latin settled on Ulixēs or (less correctly to some) Ulyssēs. Some scholars once supposed two figures fused into one; others explain the d/l variation through Etruscan Uthuze, possibly from a Minoan form with an affricate foreign to early Greek.

Homer's Odyssey opens by calling him polytropos — Murray's "man of many devices," Fagles's "man of twists and turns," Wilson's "a complicated man." He also bears the patronymic Laertiades, "son of Laertes." In Odyssey 19 Euryclea hopes Autolycus will name the infant something like Polyaretos ("much prayed for"); Autolycus instead commemorates his own lifelong anger with many men and women by choosing Odysseus.

Dares the Phrygian describes Odysseus as tough, crafty, cheerful, of medium height, eloquent and wise. In Iliad 3 Priam sees him shorter than Agamemnon but broader in chest and shoulders, like a deep-fleeced ram among the flock; Antenor recalls that seated he looked more imposing than Menelaus. The Odyssey gives him bushy hyacinth-like locks, a bronze tan, and, when he sheds his rags, fine massive thighs and brawny arms.

Homer makes him son of Laertes and Anticlea, with a younger sister Ctimene. Apollodorus traces his paternal line through Arcesius to Cephalus and Aeolus, and his maternal grandfather as the thief Autolycus, son of Hermes — though the Odyssey itself does not assert that blood link. A non-Homeric tradition held that Sisyphus was his true father and that Laertes bought the child. Later genealogies multiply his offspring beyond Telemachus (Telegonus by Circe, Nausithous and Nausinous by Calypso, and others) often to claim Italic city foundations.

Most pre-war exploits are told by late mythographers such as Apollodorus and Hyginus. When Helen's abduction summons the suitors bound by Tyndareus's oath, Odysseus feigns madness — yoking mismatched beasts to a plow, in some modern retellings sowing salt — until Palamedes places infant Telemachus in the furrow; Odysseus swerves aside and is exposed. He nurses a lasting grudge against Palamedes.

He also helps recruit Achilles on Scyros: Thetis has hidden her son among the king's daughters, but Odysseus lays out ornaments and weapons, then sounds a battle alarm; Achilles alone seizes a weapon and is unmasked. A related stratagem of mixed gifts appears in Statius's Achilleid.

In the Iliad Odysseus is among the most trusted Achaean counsellors, with Nestor and Idomeneus. He quells the army when Agamemnon tests morale, joins the embassy to Achilles in Book 9, and with Diomedes kills Rhesus in the night raid of Book 10 so that the Thracian's horses never drink from the Scamander. After Patroclus's death he urges Achilles to let the men eat before fighting. At the funeral games he wrestles Ajax to a draw and, aided by Athena, wins the foot race. He is often read as Achilles' antithesis — restraint and diplomacy against all-consuming rage — and as Ajax's foil: eloquence and mêtis against pure brawn.

Cyclic and tragic tradition adds darker exploits: arranging Palamedes' death by forged letter or by burying him in a well with Diomedes; retrieving Achilles' body with Ajax and then winning Achilles' arms in the contest that drives Ajax to suicide; fetching Neoptolemus and Philoctetes (with Heracles' bow) when oracles demand them; stealing the Palladium with Diomedes; and devising the Wooden Horse. Roman poets who claimed descent from Aeneas cast him as "cruel" or "deceitful Ulixes," valuing Greek cunning as fraud against Latin honor.

Homer's Odyssey narrates ten years of homecoming. After a raid on the Cicones, Odysseus's fleet meets the Lotus-Eaters and the Cyclops Polyphemus, whom he blinds under the alias Outis ("Nobody") before rashly revealing his name and earning Poseidon's enmity. Aeolus's bag of winds is opened by the crew in sight of Ithaca; the Laestrygonians destroy eleven ships; Circe turns men to swine until Hermes' moly protects Odysseus, who stays a year before sailing to the edge of the world to consult Tiresias among the dead.

Warned again by Circe, they pass the Sirens, lose six men to Scylla, and — against orders — slaughter Helios's cattle on Thrinacia; Zeus wrecks the ship and only Odysseus survives, spending seven years with Calypso on Ogygia until Hermes orders his release. The Phaeacians convey him sleeping to Ithaca. Disguised by Athena as a beggar, he reunites with Telemachus and Eumaeus, is recognized by the dog Argos and the nurse Eurycleia (by an old boar-hunt scar), strings his bow in Penelope's contest, and with Telemachus, Eumaeus and Philoetius slaughters the suitors. Penelope tests him with the secret of their olive-tree bed; their recognition turns on homophrosýnē ("like-mindedness"). Athena and Zeus then halt a civil war over the suitors' deaths.

The lost Telegony sent Odysseus to Thesprotia, marriage to Callidice, and eventual death at the hands of Telegonus, his son by Circe, who struck him with a stingray-tipped spear. Telegonus brings Penelope and Telemachus to Aeaea; Circe makes them immortal and pairs the households. Other ends include a heron's barb rotting an aged Odysseus's scalp (Aeschylus's lost Ghost-Raisers), resurrection and a second death from grief, transformation into a horse by Athena, or exile after Neoptolemus arbitrates the suitors' blood-feud.

Tragedy kept him central (Sophocles' Ajax and Philoctetes; Euripides' Hecuba, Rhesus, Cyclops). Plato's Hippias Minor asks whether Homer meant Achilles or Odysseus as the better man. Pausanias records Arcadian traditions of statues and a sanctuary he dedicated at Pheneus after recovering lost mares. Medieval and modern reception ranges from Dante's fraudulent Ulisse sailing past the Pillars of Hercules, to Tennyson's restless "Ulysses," to countless novels, films and operas — while folk etymology even made him founder of Lisbon (Ulisipo / Olisipo).