One of the great things about the Greek legends is that they aren't told in isolation. They are all inter-related like the episodes of a giant soap opera. Characters from one set of legends will often cross over into another. For example, Herakles (that's Hercules to you Latinates out there) was numbered among the Argonauts before he went solo with his own legends. Since he became the most popular hero of Greek legend, this was obviously a wise PR move.
The Greek legends are not just inter-related, they converge towards the climactic event of the Heroic Age: the Trojan War. This was the Big One, and anyone who was anyone in this last generation of heroes fought on one side or another of the Trojan War. This is a generalized retelling of this epic struggle by that most questionable of sources, Erroneous Hilarious the Cretan (or Cretin, depending on translation). It's not history, but it's not bad.
Guess Who We're Eating for Dinner?
Atreus and Thyestes were brothers, both sons of the king Pelops. Pelops had lots of sons, most of whom became kings (it was sort of the family business). In fact, the kinghood of the sons of Pelops was so common in southern Hellas that it is still known as the Peloponnese to this day.
At any rate, Atreus and Thyestes had a severe sibling rivalry going, so both of them were interested in being king of Mycenæ, one of the most prominent cities of the time. Atreus won out and convinced the Mycenæans to make him their king. Thyestes got revenge by seducing Ærope (Mrs. Atreus). In an ever escalating cycle of vengeance, Atreus sought revenge on Thyestes in a manner that would both emotionally scar him and make him unclean in the eyes of the Mycenæan people.
Pretending to forgive his brother of all the bad blood between them, Atreus invited Thyestes to a feast to celebrate the reunification of their families. Everything was very cordial and Thyestes, who was suspicious at first, finally came to feel that Atreus was actually letting his guard down.
At the end of the feast Atreus asked his brother how he liked the food. Thyestes replied that it was quite tasty, at which point Atreus had a platter bearing the heads of two of Thyestes' sons brought out from the kitchen and revealed the true nature of the main course. Realizing that he had eaten his own children (the finger sandwiches should have been the tipoff) Thyestes ran vomiting from the palace and laid a curse on the house of Atreus. The exact wording is uncertain, but the idea was "May something really bad happen to your kids, too." This curse would strike Atreus' sons full force and take down most of the rest of the known world with them.