Castor (or Kastor) and Polydeuces (sometimes called Pollux), were in Greek mythology the twin sons of Leda and the brothers of Helen of Troy and Clytemnestra. According to Liddell and Scott's Lexicon, kastor is Greek for "beaver", and poludeukeis means "very sweet".
They are called the Dioscuri (dios kouroi), meaning the "Sons of Zeus," although the story of their parentage is confused, as it is for their sisters Helen and Clytemnestra. The best known story is that Zeus disguised himself as a swan and seduced Leda. Thus Leda's children are frequently said to have hatched from two eggs that she then produced. By many accounts, however, Leda's mortal husband Tyndareus could also have fathered some of the children. Which children are thus mortal and which half-immortal is not consistent among accounts, nor is which children hatched from which egg. Castor and Polydeuces are sometimes both mortal, sometimes both divine. One consistent point is that if only one of them is immortal, it is Polydeuces.
As a further complication, the Zeus swan story is sometimes associated with the goddess Nemesis. In this tradition, it was Nemesis who was seduced and who laid the egg, but the egg was then found by or given to Leda. However, this story is usually associated with Helen, not with Castor and Polydeuces.
Polydeuces was a powerful boxer, and Castor a great horseman.
In Roman mythology, Castor was venerated much more often than Polydeuces. He was known as Castore.
When Theseus and Pirithous kidnapped their sister Helen and carried her off to Aphidnae, the twins rescued her and counter-abducted Theseus' mother, Aethra. They also accompanied Jason on the Argo; during the voyage, Polydeuces killed King Amycus in a boxing match.
When Astydameia, queen of Iolcus, offended Peleus, the twins assisted him in ravaging her country.
Castor and Polydeuces abducted and married Phoebe and Hilaeira, the daughters of Leucippus. In return, Idas and Lynceus, nephews of Leucippus (or rival suitors), killed Castor. Polydeuces was granted immortality by Zeus, and further persuaded Zeus to share his gift with Castor. (In some accounts, only Polydeuces was fathered by Zeus, while Leda and her husband Tyndareus conceived Castor. This explains why only Polydeuces was granted immortality.) Accordingly, the two spend alternate days as gods on Olympus and as deceased mortals in Hades.
Their festival was on July 15.
Compare with Amphion and Zethus of Thebes, with Romulus and Remus of Rome and with the Asvins of Vedic mythology. Some have supposed a general Indo-European origin for the myth of the divine twins.
The constellation Gemini is said to represent these twins, and its brightest stars Castor and Pollux (α and β Geminorum) are named for them.