Castor and Pollux were also known as Dioscuri.
In Greek and Roman mythology they were considered the twin sons of Leda. They had different fathers, Tyndareus and Zeus( the king of the gods). Leda was the wife of Tyndareus, king of Lacedaemon
It was told that Castor was the son of Tyndareus and thus was mortal, while Pollux was the son of Zeus (who famously had approached Leda in the form of a swan).
Some sources said that Castor and Pollux were born from an egg, along with their twin sisters Helen and Clytemnestra.
They were fine horsemen, and Pollux was an unrivaled boxer. Both participated in the hunting of the Calydonian boar and in the voyage of the Argo. When Theseus (well known for killing Minotaur with help of Ariadne) abducted their sister(Helen), they invaded Attica and recovered her.
Castor and Pollux fell in love with Phoebe and Hilaeira. The brothers abducted the Leucippides(Phoebe and Hilaeira) and brought them back to Sparta, thus starting a family feud.
Later Idas murdered Castor but Pollux killed Lynceus; in retribution, Zeus killed Idas with a thunderbolt.
Zeus told Pollux to choose between spending all his time on Olympus or giving half of his immortality to his mortal brother so that they could alternate realms together.
Pollux chose to share his immortality. Other sources said that they became the constellation Gemini (though several different pairs are associated with the constellation).
Many Artists portraited the twins as two youths, usually horsemen, holding spears and wearing helmets in their art.