To fully appreciate Seneca's play, it's helpful to understand the characters in the context of the ancient Greek myths and legends in which they appear.

All of the major characters in Thyestes are found in the myth of "The House of Atreus," which is also called "The Curse of the House of Atreus." Why it's called "The Curse of the House of Atreus" will become clear in a moment.

The "The House of Atreus" myth was first used as a basis for plays by the Greek playwrights Sophocles (in Electra), Aeschylus (in Choephoroi, Agamemnon, and Eumenides), and Euripides (in Iphigenia in Aulis, Orestes, and Electra).

Tantalus: Tantalus, who appears as a Ghost in Thyestes, was the son of Zeus and Pluto, or Plouto (the Greek nymph, not the planet or the Disney character).

Tantalus thought it would be a great idea to kill his son, Pelops, and serve his body as a main course in a banquet for the gods, to test whether or not the gods could discover his trick.

They did, and they were not pleased. The gods brought Pelops back to life, but they sent Tantalus to the underworld and condemned him to the eternal punishment of being "tantalized" forever by food and drink which was kept just out of his reach.

This is the beginning of "the curse" on Tantalus' descendants that they would kill each other, and feed children to their relatives.

Atreus: Atreus is the eldest son of Pelops, by then King of Pisa. Pelops had acquired the throne through trickery—a common occurrence in this myth—which resulted in the death of the rightful King, and another curse was laid on the family.

The area of the Peloponnese in southern Greece is named after Pelops. The cities of Pisa, Sparta, Corinth, Argos and Megalopolis are located on the Peloponnese, and it was the scene of the Peloponnesian Wars of 431–404 BC.

Thyestes and Chrysippus: Pelops had two other sons, Thyestes, and Chrysippus. Atreus and Thyestes killed Chrysippus to please their mother and hoped by Chrusippus' death to ascend together to their father's throne in Pisa.

Instead, Pelops banished them, and they fled to Mycenae.

After some trickery—trickery again—involving a golden fleece (not the fleece from the myth of "Jason and the Golden Fleece"), Thyestes became King of Mycenae.

However, Atreus believed that Zeus wanted him to be King, and Atreus said that he would prove it by making the sun rise in the west and set in the east. When this actually happened, Atreus was named King, and Atreus banished Thyestes from Mycenae when he discovered that Thyestes had an affair with his wife, Aerope—who was also involved with the earlier trickery with the golden fleece.

Ghost of Tantalus and Megaera: At this point in the myth, Seneca's play, Thyestes, begins, with the Ghost of Tantalus being summoned from the underworld by Megaera, one of the Furies (also known as the "Erinyes" or the "Eumenides," female goddesses of vengeance), who orders him to wreak havoc in Atreus's kingdom by bringing "the curse" to to bear on Atreus and Thyestes.

Tantalus reluctantly wreaks havoc on the kingdom and brings "the curse" to Atreus, Thyestes, and their families, and the result of his efforts is the plot of Thyestes.

Thyestes's sons: Having vowed vengeance against Thyestes, Atreus devises a plan to kill Thyestes's sons—ironically, one of whom is named "Tantalus" in the play—cook them in a soup, and trick Thyestes into eating the soup, which he does.

Atreus and Thyestes thereby fulfill "the curse," which has become known not as the curse of Tantalus, who started it all, but as "The Curse of the House of Atreus."

"The curse," and the myth, continue for two more generations and involve Atreus's sons, Agamemnon and Menelaus, two of the most famous characters in Greek mythology, who also appear in a number of ancient Greek and Roman plays—including Agamemnon by Seneca himself.