To be more specific, Oedipus is the king of Thebes, a position he inherited when, wandering from his home in Corinth, he encountered the Sphinx, who was eating any Theban who could not answer his riddle. Oedipus answered it, and saved the city, and now has married its queen Jocasta, the former king being recently murdered. A plague has struck the city, and the oracle of Apollo says that it will only pass when the former king's murderer is put to justice. With the help of the prophet Teiresias, Oedipus discovers that he is the murderer, recalling a fight in which he killed an unknown man years ago, and that he is really Jocasta's son, expelled from Thebes as an infant because of a prophecy that said he would do exactly what he ends up doing.
But it is, of course, the essential work of ancient Greek tragedy. It is the most oft-used example Aristotle gives when he outlines tragedy for us in the Poetics, suggesting that shows remarkable purity of genre. All the elements are there: a hero is neither a great man nor a villain, but the bearer of a fatal flaw that eventually leads to his downfall. There is a startling revelation (peripeteia), a sudden reversal of fortune (anagnorisis), and an ending so bleak and ruinous that you might call it a catastrophe (catastrophe).
Of course, it is also the basis for Freud's theory of the Oedipal complex, making it one of the most essential texts in the development of Freudian criticism and literary criticism as a whole. In this way, its relevance spans a vast stretch of time, and it is an excellent illustration of the way that we regard literature differently than our predecessors.
Unlike The Odyssey, I find Oedipus the King wanting for emotional heft to complement its academic fecundity. All tragedies are meant to act as funhouse mirrors in which we see ourselves, but Oedipus' basic humanity is less apparent to me than Odysseus', whose longing for his home and his wife is truly affecting. One issue may be the translation, which I feel is a little banal. See the way that this translator, Benard Knox, renders Oedipus' opening address to the priests who are gathered in supplication to the gods:
My sons! Newest generation of this ancient city of Thebes! Why are you here? Why are you seated there at the altar, with these branches of supplication? The city is filled with the smoke of burning incense, with hymns to the healing god, with laments for the dead.
Contrast Sir George Young:
Children, you modern brood of Cadmus old,
What mean you, sitting in your sessions here,
High-coronalled with votive olive-boughs,
While the whole city teems with incense-smoke,
And paean hymns, and sounds of woe the while?
Knox's translation, besides committing the terrible sin of being in prose, is awfully clumsy and plain, isn't it? Not only that, but you get the impression a lot of the syntax is lost here--see how Oedipus' statement about the incnese is subordinated in Young's translation, suggesting that Oedipus is asking about that as well as the priests' presence, and in Knox's it is presented as a flat statement unconnected to anything. Stupid.
But whatever. One benefit of Oedipus is that it's literally one-tenth the size of The Odyssey, so in my class we can really pick it apart and deconstruct it. I wish it were made of better stuff, but what can you do?