The Odyssey is the second of the two great Greek epic poems ascribed to Homer, the first being the Iliad. It describes the adventures of Odysseus as he and his crew travel back to his native Ithaca from Troy after the Trojan War, a voyage that took them twenty years and brought them to various people and places. They suffer various misfortunes brought about by Poseidon, encountering, among others: Aeolus, Calypso, Circe, Hades, Ino, the Lotus-Eaters, Polyphemus the Cyclops, Scylla and Charybdis. None of his crew survive the voyage.
Coming home, he finds that his palace is being occupied by men trying to marry his supposedly widowed wife Penelope. Penelope does not believe he is dead, and doesn't want to remarry: she has put the suitors off by insisting that she must first weave her husband a burial shroud, and every night she undoes that day's weaving. After posing for a while as a beggar, Odysseus reveals himself and kills them all.
In the English language, the word odyssey has come to refer to such epic voyages.
The movie O Brother, Where Art Thou has the basic plot of the Odyssey, and was probably inspired by it.