The family was subject to a curse beginning with Tantalus.
Tantalus killed his own son and served him to Zeus and the Olympians at a banquet. He was punished for this by having to stand in a pool in Tartarus, surrounded by trees. When he tried to drink, the pool would drain itself and when he tried to eat a fruit from the tree, the branches would move out of his reach. From hsi name comes the word "tantalize".
Tantalus was the son of Broteas and also suffered due to the curse put on his namesake. He was overthrown as King of Lydia and the Heraclidae began their rule.
Niobe was Tantalus' daughter. She married Amphion and bore fourteen children (the Niobids), seven girls and seven boys. She taunted Leto becuase the goddess only had two children. When Leto's children, Apollo, and Artemis grew up, they shot and killed the Niobids. Niobe then fasted for four days and Leto turned her to stone. Her stone form, the Weeping Rock, can still be seen near Mt Sipylus, Turkey.
Pelops was brought back to life by Zeus and eventually won the hand of Hippodamia in marriage, but at the cost of his father-in-law's life in a chariot race. Also, his father-in-law's charioteer cursed the family with his dying breath.
Atreus was Pelop's eldest son and was married to Aerope, who eventually deserted him for his brother Thyestes. When Thyestes exiled him from Mycenae, he eventually returned but was killed by Aegisthus, his nephew/grand-nephew (Aegisthus' father was Thyestes, his mother was Thyestes' daughter Pelopia).Pelopia. When he consulted an oracle on how to have a son, he was told to rape his daughter. Out of their incestuous union came Aegisthus. was eventually killed by his brother's two sons.
Atreus' eldest son - when Agamemnon returned from Troy, he was killed by his wife Clytaemnestra, and her new lover Aegisthus, his own cousin.
Aegisthus was Thyestes' son/grandson and was murdered by Orestes after he committed adultery with Clytaemnestra and killed Agamemnon
Orestes was the last victim of the curse. He killed his mother and Aegisthus after they murdered his father. He was plagued by the Furies but eventually cleared of the charges of matricide.
Orestes' son was the last Atreid monarch, being defeated by the Heraclidae, who returned to claim the Peloponessus as the rightful inheritance of their famed ancestor.