In Sophocles' 'Oedipus Rex,' King Oedipus seeks to save Thebes from a devastating plague, which is revealed to be punishment for the murder of the previous king, Laius. As he uncovers the truth, he discovers that he is the murderer and has unwittingly married his mother, Jocasta, leading to despair and tragedy. Ultimately, Oedipus blinds himself and accepts his fate, asking to be exiled due to the horrific revelations of his actions.