Twin brothers with different fathers, and one immortality split between them
Castor and Pollux shared a mother, Leda, but in the best-known version only Pollux was the son of Zeus. When mortal Castor was killed, Pollux gave up half his immortality so they could stay together, alternating days between Olympus and the underworld. They became the two brightest stars of Gemini.
The twins, known together as the Dioscuri, have a tangled family tree. Homer's Odyssey makes them sons of the Spartan king Tyndareus, a poem attributed to Hesiod calls them sons of Zeus, and Pindar's compromise gave Castor a mortal father and Pollux a divine one, Zeus having come to Leda as a swan. Some accounts have them hatching from an egg together with their sister Helen of Troy. In the Iliad, Helen scans the Greek army from the walls of Troy for her brothers, unaware they are already dead and buried at home.
They were heroes of action. Both hunted the Calydonian Boar and sailed with Jason on the Argo, where Pollux beat King Amycus in a boxing match. When Theseus carried off Helen, they invaded Attica, rescued her and took Theseus's mother back to Sparta. Their end grew out of a family feud: after their cousins Idas and Lynceus cheated them over a stolen herd of cattle, the twins went to take revenge, and the keen-eyed Lynceus spotted Castor hiding in a tree. Idas speared Castor, Pollux killed Lynceus, and Zeus struck Idas down with a thunderbolt. One tradition says the cousins' absence from a Spartan feast left Helen alone with Paris, helping set the Trojan War in motion.
Sailors prayed to the pair for fair winds and saw them in St Elmo's fire, and their skill as riders and boxers made them patrons of athletes. Artists showed them as helmeted horsemen, and the pointed caps they wear on vases were explained in antiquity as leftover shell from their egg.
Sparta treasured them most. The city's unusual system of two kings mirrored the twins, and a symbol of two upright posts joined by crossbeams was carried before the army. After both kings bungled an invasion of Attica in 504 BC, Sparta ruled that only one king would lead the army, taking just one image of the twins with him. Spartans swore their standard oath by the two gods.
Source: Castor and Pollux