When Oedipus stepped down as King of Thebes, he gave the kingdom to his two sons, Eteocles and Polynices, who both agreed to alternate the throne every year. However, they showed no concern for their father, who cursed them for their negligence. After the first year, Eteocles refused to step down and Polynices attacked Thebes with his supporters (the Seven Against Thebes). Both brothers died in the battle. King Creon, who ascended to the throne of Thebes, decreed that Polynices was not to be buried. Antigone, his sister, defied the order, but was caught. Creon decreed that she was to be buried alive, this in spite of her betrothal to his son Haemon. Antigone's sister, Ismene, then declared she had aided Antigone and wanted the same fate. The gods, through the blind prophet Tiresias, expressed their disapproval of Creon's decision, which convinced him to rescind his order, and he went to bury Polynices himself. However, Antigone had already hanged herself rather than be buried alive. When Creon arrived at the tomb where she was to be interred, Haemon attacked him and then killed himself. When Creon's wife, Eurydice, was informed of their death she too took her own life.
See also Epigonoi
There was another person in Greek mythology named Creon. He was a King of Corinth and father of Creusa and Glauce. His wife sold Tisiphone into slavery.
Creon was also the first Archon of Athens after the position was limited to a term of one year, in 683 BC.