The House of Atreus began with Tantalus, son of Zeus, who murdered his son, Pelops, and attempted to feed him to the gods. The gods, however, were not tricked and banished Tantalus to the Underworld and brought his son back to life. Later in life Pelops and his family line were cursed by Myrtilus, a son of Hermes, catalyzing the curse of the House of Atreus. Pelops had two children, Atreus and Thyestes, who are said to have killed their half-brother Chrysippus, and were therefore banished.
Thyestes and Aerope, Atreus’ wife, were found out to be having an affair, and in an act of vengeance, Atreus murdered his brother's sons, cooked them, and then fed them to Thyestes. Thyestes had a son with his daughter and named him Aegisthus, who went on to kill Atreus.
Atreus’ children were Agamemnon, Menelaus, and Anaxibia. Leading up to here, we can see that the curse of the House of Atreus was one forged from murder and deceit, and continued in this way for generations through the family line. To put it simply, the curse demands blood for blood, a never ending cycle of murder within the family.
Those who join the family seem to play a part in the curse as well, as seen in Clytemnestra when she murders her husband Agamemnon, in revenge for sacrificing their daughter, Iphigenia. Orestes, goaded by his sister Electra, murders Clytemnestra in order to exact revenge for her killing his father.
Orestes is said to be the end of the curse of the House of Atreus. The curse holds a major part in the Oresteia and is mentioned in it multiple times, showing that many of the characters are very aware of the curse's existence. Aeschylus was able to use the curse in his play as an ideal formulation of tragedy in his writing.