Sophocles is regarded as one of the three great ancient Greek tragedians, together with Aeschylus and Euripides. He wrote 123 plays of which his Theban plays (Oedipus Rex, Oedipus at Colonus and Antigone) are best known.  
During Sophocles’ lifetime dramatic competitions were held at the Festival of Dionysus. Playwrights submitted four plays -- three tragedies and a lighter ‘satyr’ play. The great poets of the day competed for the prizes each year. Sophocles he won more first prizes than any other playwright (about 20), and placed second in all others he participated in Contrary to popular belief the Theban plays are not a trilogy and were actually written over a 40 year period. Only seven of his tragedies have survived complete in the medieval manuscript tradition.
Sophocles was born close Athens. The young Sophocles won awards in wrestling and music, and was a musician of some note. He led the chorus of naked boys (paean) at the Athenian celebration of the victory against the Persians at the Battle of Salamis in 480 BC.
Sophocles was also a well known public figure as well as a playwright and served as one of the treasurers of Athens. He was elected general in 410, and he participated in the crushing of the revolt of Samos.
The three plays which make up the Theban cycle follow the tragic downfall of the mythical king Oedipus of Thebes and his descendants. They were written over Sophocles' life with Antigone probably written first. There are a number of inconsistencies although the plays are rarely performed together and thus are of little importance.
The theme of the plays, however, are consistent in dealing with fate, guilt, and divine and human justice.

The Theban Plays (spoiler alert)

Oedipus Rex
Most ancient Greeks would already know the legend of Oedipus. The legend goes that in the city of Thebes the baby son of King Laius and Queen Jocasta, is sent to be exposed and left for dead on a mountainside in an effort to avoid a prophecy that said the son would kill his father. However, he was found by a shepherd and raised in the court of King Polybus and Queen Merope of Corinth. Hearing from an oracle that he was destined to kill his father and marry his mother, and believing Polybus and Merope to be his real parents, Oedipus left Corinth. Meeting Laius by chance on a road and not recognizing him, Oedipus became involved in a fight with Laius and killed him. Oedipus then makes his way to Thebes where he finds the city under siege by a Sphinx who can only be defeated by solving its riddle. Oedipus solves the riddle, the Sphinx is defeated and his reward is the kingdom of Thebes and the hand of the widowed Queen Jocasta.
The play begins after Thebes has been struck with a plague by the gods in outrage at Oedipus' unintentional wrongdoing. The play shows Oedipus' investigation into Laius’ murder. The blind prophet Tiresias explicitly tells Oedipus at the beginning of the play that Oedipus is the cause of the plague, but he refuses to understand and accuses Tiresias of conspiring with Creon, Jocasta's brother, to overthrow him.
Oedipus then calls for a former servant of Laius, the only witness of the murder, who fled the city when Oedipus became king. Soon a messenger from Corinth also arrives to inform Oedipus of the death of Polybus, whom Oedipus still believes is his real father, until the messenger informs him that he adopted. Slowly the truth emerges and the court begins to realize what has happened. Jocasta runs off and hangs herself; Oedipus learns more slowly, but upon understanding the shocking truth Oedipus  runs off and discovers Jocasta’s body. He grief he blinds himself with Jocasta’s brooches. The play ends with Oedipus entrusting his children to the care of Creon and going into exile.

Oedipus at Colonus
Is a much more sedate play with little of the dramatic elements of the opening play. The play was proably the last of the three and is more like a long discussion than a play.
The blinded Oedipus has come with his daughters Antigone and Ismene to Theseus, the king of Athens.
Creon however has followed him to Colonus to claim Antigone and Ismene, whom Oedipus entrusted to him after his exile. Creon and his men seize the two daughters but they are rescued by Theseus and Creon is driven off. Theseus then informs Oedipus his son Polyneices, who has been banished from Thebes by his brother Eteocles, has come to Athens to talk to Oedipus.
In their philosophical talk, Oedipus discusses his fate as related by the oracle, and claims that he is not fully guilty because his crimes of murder and incest were committed in ignorance.
Following their conversation there is a fierce thunderstorm, which Oedipus interprets as a sign from Zeus of his impending death. His death is not shown on stage but the events are recounted by a messenger and Oedipus is absolved and taken away by Zeus.

Antigone
In many ways, Antigone is a revolutionary play. It is the first to have action take place inside a palace. Most plays up this date took place on the steps of the palace. It also introduces the character of The Sentry who, much like similar characters in Shakespeare’s plays, acts as a second chorus and speaks as lower class person.
As with many plays, the legend of sons of Oedipus would already be widely known. With Oedipus in exile, Thebes is ruled by his two sons, Eteocles and Polynices who must take it in turns to rule. Eteocles rules first but the two become enemies after Eteocles refuses to give up the throne, and Polynices is exiled.
The play open with both brothers are dead, slain by the other's hand. Oedipus is dead and the daughters are back in Thebes. Creon now becomes King and makes a decree that since Polynices fought against Thebes, he shall not be buried. Meanwhile, Eteocles is to be buried with full military honors.
As the daughter of Oedipus and the sister of the dead brothers, Antigone believes this proclamation to be against the gods' orders. She plots with her sister to bury Polynices herself but Ismene refuses to take part out of fear of Creon.
When Creon is informed that someone is trying to bury Polynices, he make a terrible threat and when Antigone is caught going to her brother’s body she and brought before the furious king. Defiantly, she accepts her death sentence. Ismene stands with her sister and admits to taking part in the crime.
Antigone's fiancé and Creon's son Haemon arrives and argues with his father over the sentence. Enraged, Creon orders Antigone be starved to death in a sealed cave. The chorus persuades him to let Ismene go.
The prophet Tiresias emerges and tells Creon that his actions are contrary to the gods and soon his own flesh and blood will die, and his actions are cursing the entire city. Scared of this terrible prophecy, Creon is torn but finally agrees that Polynices must be buried and Antigone must be freed.
But Antigone has already hanged herself in her cave. Haemon rushes to save Antigone, but is too late. Creon arrives too but is confronted by the grieving Haemon who threatens to kill Creon but turns his sword on himself. Haemon's mother and Creon's wife, Eurydice, also kills herself in grief.
Creon, now having lost all of his family, collapses in despair and is led from the stage.