Revenge drives all of the action in Electra. The family history involves a horrific crime and most of the tragedies which follow are crimes committed to compensate for an earlier crime. Agamemnon sacrifices Iphigeneia, for which Clytemnestra kills him. For her crime, Orestes kills his mother, for which he is pursued by the Furies (although this aspect of the legend is not addressed in Sophocles's drama).
Public vs. Private Life
Since tragedy, according to Aristotle's definition in his Poetics, involves a central figure of more than common stature, key figures are often kings or other prominent political or national figures. Consequently, this makes it possible to interpret tragedies as both explorations of private psychology and public politics. For example, William Shakespeare's Hamlet is about murder, revenge, and madness, but it is also about the failure of proper political succession and ill-gotten power (Hamlet's uncle murders his brother the king, marries his widow, and assumes the throne, bypassing Hamlet's birthright of ascendancy). The same is true of Electra, where, after Agamemnon's death, his son Orestes should have assumed the throne. The play then becomes one about the usurpation of power, and in that sense, merges public and private action.
Guilt and Innocence
The issue of guilt in Electra depends on the perspective from which one evaluates the actions. Is Clytemnestra guilty of murdering Agamemnon for political/romantic reasons (so she may marry Aegisthos who will assume her dead husband's monarchy) or is she simply avenging her daughter's sacrifice? Is Orestes guilty of Clytemnestra's murder for similar political reasons or is he merely executing her for murdering his father, Agamemnon? Ultimately, guilt or innocence is central to the world of Greek tragedy, where characters are destined by the gods but also act freely.
Duty and Responsibility
This theme becomes particularly complex in Electra, where various characters often have contradictory, even mutually exclusive responsibilities. For example, as a father, Agamemnon must protect his daughter, Iphigeneia, but as a king, his duty is to sacrifice her for the good of his kingdom. As a son, Orestes must love his mother, but also as a son, he must avenge his father's murder.