The gods Apollo and Poseidon, during a time when they were being punished by having to work among men, built the city of Troy for Priam's father, Laomedon. They invited the mortal man Aeacus (the son of Zeus and Aegina and grandfather of Achilles) to help them, since destiny had decreed that Troy would one day be captured in a place built by human hands.
When newly constructed, Troy was attacked and captured by Herakles (Hercules), Telamon (brother of Peleus and therefore the uncle of Achilles; father of Telamonian Ajax and Teucros), and Peleus (son of Aeacus and father of Achilles), as a punishment for the fact that Laomedon had not given Hercules a promised reward of immortal horses for rescuing Laomedon's daughter Hesione. Telamon killed Laomedon and took Hesione as a concubine (she was the mother of Teucros).
Priam, King of Troy and son of Laomedon, had a son from his wife Hekabe (or Hecuba), who dreamed that she had given birth to a flaming torch. Cassandra, the prophetic daughter of Priam, foretold that the new-born son, Paris (also called Alexandros), should be killed at birth or else he would destroy the city. Paris was taken out to be killed, but he was rescued by shepherds and grew up away from the city in the farms by Mount Ida. As a young man he returned to Troy to compete in the athletic games, was recognized, and returned to the royal family.
Peleus (father of Achilles) fell in love with the sea nymph Thetis, whom Zeus, the most powerful of the gods, also had designs upon. But Zeus learned of an ancient prophecy that Thetis would give birth to a son greater than his father, so he gave his divine blessing to the marriage of Peleus, a mortal king, and Thetis. All the gods were invited to the celebration, except, by a deliberate oversight, Eris, the goddess of strife. She came anyway and brought a golden apple, upon which was written "For the fairest." Hera (Zeus's wife), Aphrodite (Zeus's daughter), and Athena (Zeus's daughter) all made a claim for the apple, and they appealed to Zeus. He refused to adjudicate a beauty contest between his wife and two of his daughters, and the task of choosing a winner fell to Paris (while he was still a herdsman on Mount Ida, outside Troy). The goddesses each promised Paris a wonderful prize if he would pick her; Hera offered power, Athena offered military glory and wisdom, and Aphrodite offered him the most beautiful woman in the world as his wife. Paris gave the apple, in the famous Judgement of Paris, to Aphrodite.
Helen, daughter of Tyndareus and Leda, was also the daughter of Zeus, who had made love to Leda in the shape of a swan (she is the only female child of Zeus and a mortal). Her beauty was famous throughout the world. Her father Tyndareus would not agree to any man's marrying her, until all the Greeks warrior leaders made a promise that they would collectively avenge any insult to her. When the leaders made such an oath, Helen then married Menelaus, King of Sparta. Her twin (non-divine) sister Klytaimnestra (Clytaemnestra), born at the same time as Helen but not a daughter of Zeus, married Agamemnon, King of Argos, and brother of Menelaus. Agamemnon was the most powerful leader in Hellas (Greece).