The play begins outside the Greek city of Argos, some years after the end of Agamemnon, Part 1of Aeschylus's Oresteia trilogy. Orestes, the son of Agamemnon, has come back home from exile to avenge Agamemnon's death. Orestes is accompanied by a friend, Pylades. Agamemnon was murdered by his own wife, Clytemnestra, who is also Orestes's mother. Clytemnestra had help in her plot from Aegisthus; they are now living together as lovers. Orestes cuts off two locks of his hair to make as offerings: he gives one as an offering to a river in Argos, and the other to the spirit of his father. After he makes these offerings, Orestes sees his sister Electra coming up to the tomb of Agamemnon, along with a group of slave-women. Orestes and Pylades take up positions in hiding to see what happens next.
When Electra comes to the tomb, she makes a speech revealing that it was Clytemnestra who sent her and the slave-women to make the offerings. Electra feels awkward because she doesn't know what she can say to her father's spirit on Clytemnestra's behalf; everything seems inappropriate, since it is coming from Agamemnon's murderer. She asks the Chorus (i.e., the group of slave-women) for advice. After some back and forth, they tell her to pray that Orestes will come from abroad to avenge Agamemnon's death. After Electra makes this prayer, she notices the locks of hair that Orestes left on the tomb. She can't think of anybody who would want to make such an offering other than her brother Orestes. Then she notices that the hair looks like her own hair, and the footprints around the tomb match her own as well! (Since when do brothers and sisters have identical footprints? Hmm. We'll just ignore that for now.)
Electra is half-convinced that Orestes has returned, but half-convinced that it's impossible that he came. At just this moment, Orestes and Pylades step forward and reveal themselves. Orestes reveals that an oracle of Apollo told him that he had to go to Argos and avenge his father – otherwise the gods would punish him with horrible diseases. Orestes, Electra, and the Chorus join together in singing and chanting prayers to Agamemnon, asking for his help in getting revenge on Clytemnestra and Aegisthus.
When they are finished singing this song, Orestes asks Electra and the Chorus, "So, why'd you guys pick this day to come offer libations to Agamemnon, anyway?" The women of the Chorus explain that Clytemnestra sent them because of a horrible dream she had: she dreamed that she gave birth to a snake; when she put the snake to her breast, it drew blood out along with the milk. Orestes thinks this is great news – he interprets himself as the snake, because he is coming to kill his own mother.
With this new burst of confidence, Orestes takes charge of the situation: he tells Electra to go inside the palace and act natural; he also asks the Chorus to help him out by saying the right things at the right time. Then Orestes and Pylades go up to the gate of the palace and start knocking to be let in. Finally, Clytemnestra comes out. Orestes, pretending to be a traveler from Parnassus (near Delphi, where Apollo's temple is), tells Clytemnestra: "On my way here I ran into a man who told me that your son Orestes is dead. Sorry." Clytemnestra acts as if she is sorry to hear this, but welcomes Orestes (as the traveler from Parnassus) and Pylades into the house anyway.
This leaves the Chorus of slave women standing onstage alone. Just then, Orestes's old Nurse runs by. She is horrified at the news that the baby she once nursed has now grown up and died. It turns out that the Nurse is on her way to get Aegisthus and bring him to the palace. The Chorus convinces the Nurse to modify the message she brings to Aegisthus: she is to tell him to come to the palace, but without any bodyguards. Not long afterwards, Aegisthus shows up, alone, to get the scoop from Orestes. Orestes seizes the opportunity and kills Aegisthus (offstage).
When a slave runs out of the house screaming that Aegisthus has been murdered, Clytemnestra comes out to see what all the commotion is about. Just when she realizes what has happened, Orestes and Pylades come toward her, out of the house. Orestes is about to kill his mother, but her words make him hesitate. Then Pylades, who has not spoken yet in the whole play, urges Orestes to go ahead and do it. After a little bit more chit-chat, Orestes leads Clytemnestra into the palace and kills her.
A short time later, Orestes opens the palace gates to reveal himself standing over the dead bodies of Clytemnestra and Aegisthus. (This parallels the end of Agamemnon, when Clytemnestra stands in the palace gates over the dead bodies of Agamemnon and Cassandra.) He commands some slaves to stretch out a fabric, which Clytemnestra threw over Agamemnon to trap him before stabbing him. Almost immediately, though, Orestes starts to lose his mind. He becomes convinced that he is being pursued by the Furies – female spirits of vengeance. The Chorus tries to calm him down, but doesn't succeed. Orestes runs off to Delphi to be purified; the Chorus ends the play by praying that everything will turn out well.