The ancient Greeks believed that humans are not in control of their lives but that the gods act according to their own purpose, and this results in...

The most obvious irony in Oedipus Rex is that Oedipus, the king of Thebes, spends basically the entire play looking for himself.  The countryside and citizens suffer from several plagues: there is a blight on the crops, women cannot conceive, and so on.  As a result, Oedipus sends his brother-in-law Creon to the oracle of Delphi to find out what they should do, and she says that they must find the man who killed Laius, the king who ruled before Oedipus (and Oedipus's father, though he does not know this), and this will end their problems.  Therefore, Oedipus decides that he will seek this man and exile him, and, in doing so, help himself in case the man should decide to return at kill Oedipus too.  However, he doesn't realize that he is the man who killed Laius or that Laius is his own father.  Thus, Oedipus spends the entire play seeking himself, ignorant of the truth.