That the play ends on a happy note may surprise modern readers, to whom the word tragedy denotes a drama ending in misfortune. The word did not carry this meaning in ancient Athens, and many of the extant Greek tragedies end happily.
Social progress and justice
The ancient law of the Erinyes mandates that blood must be paid for with blood. The chorus states this fact several times throughout the play, most clearly in the first section of the kommos. Vengeance is just, they say, and it has been the law of the house for generations. Nothing else can wash away a bloodstain but more blood, which in turn requires more blood in order to be cleansed. The chorus offers no solution to this dire situation of violence breeding more violence. They merely state it as the natural law. However, over the course of The Libation Bearers, one has the sense that this time, things will be different. Apollo has promised Orestes that he will not suffer for his crime, and we know that a god is unlikely to go back on his word.
Since Apollo has thrown his weight behind the path of vengeance, Orestes chooses to comply with his commands. In fulfilling his duty towards Apollo and his father, Orestes condemns himself to suffering. He chooses to make this sacrifice, however, in order to preserve the laws of society. In the end of Eumenides, Orestes is tried in court by the Furies, with the goddess Athena and the Athenian elders acting as the jury. In this case, Orestes is not killed in turn for his crimes as would have been the retributive law at the time, but he is given the opportunity to defend himself, and is ultimately declared not guilty. The Erinyes are angered by this decision as they belong to the old gods, and for decades uncounted blood had to be repaid in blood. Yet Athena calms them with great effort, making it clear to them that a society cannot possibly work and grow under such circumstances, and grants them seats of great power in Athens. Justice is decided by a jury, representing the citizen body and its values and the gods themselves, who sanction this transition by taking part in the judgment, arguing and voting on an equal footing with the mortals. This theme of the polis self-governed by consent through lawful institutions, as opposed to tribalism and superstition, recurs in Greek art and thought. Athena, the goddess of Reason and Protection, calms the Erinyes, the goddesses of revenge and remorse, thereby establishing a legal system centered in Athens, relieving the Greeks of their responsibility to avenge violence with violence. Now the state is the institution to administer justice, employing reason, but also holding the power to punish, violently if need be. Athens has left its barbaric system of blood for blood behind and has embraced an order where people deserve a fair trial.
"Philos-aphilos" (φίλος ἄφιλος; "love-in-hate") is a vigorous force throughout the trilogy. Most of the bloodshed throughout the play is “murder committed not against an external enemy but against a part of the self.”  This can be interpreted literally: Orestes slays his mother, his own flesh and blood; Aegisthus is Clytemnestra's accomplice in the murder of his cousin Agamemnon, and Agamemnon had killed his daughter Iphigenia, even as a required sacrifice.
"A part of the self" can also be interpreted more figuratively as a significant other, such as a spouse; thus, Clytemnestra'’s feelings for Agamemnon are characterized as ‘philos-aphilos’ as well. As Richmond Lattimore defined it thus, “the hate gains intensity from the strength of the original love when that love has been stopped or rejected.” Clytemnestra's love for Agamemnon has been quashed by his sacrifice of Iphigenia and his return with Cassandra as a concubine. Likewise, Orestes’ sentiments toward his mother are intensified by anger at her murder of his father and resentment at the fact that she chose her lover over her children – essentially, they are “the price for which she bought herself this man.” These conflicting feelings are embodied in Clytemnestra's dream about nursing the snake.
Lattimore also draws a parallel between the Oresteia and William Shakespeare's Hamlet, suggesting that the sensation of ‘philos-aphilos’ engendered by Prince Hamlet’s emotional connections to his mother, Queen Gertrude, and to Ophelia, who are both on the side of King Claudius – himself a close blood relative who might have held Hamlet’s affection and regard before usurping the throne – are what make the play a tragedy.