In Sophocles' Oedipus the King, Creon is the brother of Jocasta and thus the brother-in-law of Oedipus, the king of Thebes.
At the first of the play, Creon, at the request of Oedipus, has traveled to Delphi to learn from the Delphic oracle how to deal with the plague ravaging Thebes. Here, Creon appears as the loyal assistant of Oedipus.
Later, though, after Teiresias declares that Oedipus is the cause of the plague, because he killed Laius, Oedipus becomes enraged and concludes that Teiresias and Creon are conspiring against him. Now, Oedipus believes that Creon wants to become the king of Thebes.
When Creon hears of this accusation, he is deeply troubled and tries to defend himself before Oedipus. His brother-in-law does not believe him, though, and a heated argument occurs between the two men. Oedipus becomes so angry that he wants Creon to go into exile and to die ("I want you to die, not just run off"; Ian Johnston translation). The encounter ends with Creon leaving, but declaring that "I’m a reasonable man."
Having moved from a trusted assistant to an accused traitor, Creon, by the end of the play, is going to serve as the interim king of Thebes. After Oedipus discovers his true identity and blinds himself, Creon is now in control of Oedipus. Creon is the one who now controls Oedipus' access not only to Thebes, but also to his daughters. As the play ends, Oedipus begs Creon for access to his daughters, but Creon, now in the position of authority over his former king, states,
Don’t try to be in charge of everything.
Your life has lost the power you once had.