Leda, the Queen of Sparta, and wife to the king Tyndareus, was greatly admired by Zeus. He considered her very beautiful. He was right, of course, as he always was concerning the beauty of women. When he set his mind to it, he always succeeded in seducing the fairer sex.
As such, Zeus transformed himself into a swan, and made haste to Sparta.
Zeus flew through the Spartan air, until he saw her standing serenely on her balcony — the lovely Leda. His attention focused intently on the Spartan queen, he didn't notice the eagle position itself above him. It glided momentarily above Zeus before dive-bombing the god.
The two birds swirled toward the ground in a tornado of feathers. Zeus managed to break away from his pursuer, and flew as fast as he could into the open arms of Queen Leda.
Leda hurried the swan into her chamber. Careful not to wake her sleeping husband, Leda carried the swan out of the room and into another suite. Looking over the swan, she noticed it's feathers were mangled, but it was otherwise unharmed.
After fixing the swan's feather, Leda made to release the swan when it spoke to her in thanks. Leda, shocked at hearing a bird speak, stopped moving. The swan continued speaking, and revealed his true identity as Zeus. The swan confessed his attraction and admiration for Leda, and leaped into her arms.
It came to be that Leda lay with the god in his swan form on the same night that she had been with her husband. The result of this affair came in the form of two golden eggs.
The first egg hatched two girls: Helen and Clytemnestra. Helen, golden and beautiful, was quite obviously the spawn of Zeus. This pleased the god so much, that he created the constellation Cygnus in her honor. Clytemnestra was no doubt Tyndareus's daughter, with her dark hair and eyes.
The second egg hatched, and from within sprung two boys: Castor and Pollux. Pollux, fair and golden as Helen, was the child of Zeus. Castor, dark and olive-skinned was the mortal child of Tyndareus.
Their different fathers never deterred the half-brothers from forming a bond, and they became inseparable throughout life. They were dubbed Dioscuri, and vowed never to be apart.
As they got older, the twins became renowned horsemen and hunters. When the goddess Artemis sent a boar to destroy Calydon, the twins eagerly joined the hunt.
It was during this hunt that Castor and Pollux met the hero Jason. They joined Jason on his ship Argo, and set off on his expedition for the Golden Fleece.
During this expedition, the Argonauts passed through Bithynia, meeting the savage King Amycus. During their time with there, King Amycus held a boxing contest. Pollux eagerly entered. As the two squared off, Pollux quickly moved in and overcame the king, killing him with a blow from his elbow.
Eventually, the Dioscuri returned from their adventure with Jason.
Upon returning, the twins learned their sister Helen had been abducted by the king of Athens, Theseus. Theseus planned to keep the girl until she was old enough to wed. Angered upon learning of this, the twins made their way to Athens whereupon they invaded the kingdom, and rescued their beloved sister. In retribution, the brothers forced Aethra, the mother of Theseus, into Helen's servitude.
But perhaps the twins' most substantial adventure were their actions that set into motion the events leading to the Trojan war.
Castor and Pollux were the cousins of the twins Lynceus and Idas. Lynceus and Idas were betrothed to the sisters Phoebe and Hilaeira. The Dioscuri had aspirations to marry the sisters, but were disliked by the girls' father, Leucippus. Desperate to have the sisters as their own, the half-brothers stole the girls away to Sparta. There, the two couples created their own families.
This upset Lynceus and Idas for obvious reason, and the cousins began a family rivalry.
One day while herding in Arcadia, the four cousins could not settle on the division of the herd. Idas suggested a contest; whoever could eat their meat first could keep the entire herd. The Dioscuri agreed, but were shocked when Idas ate both his portion of the meat as well as his brother's Lynceus' all at once. The twins reluctantly gave over the herd, and promised to get even someday.
That day came during a feast in Sparta. As everyone was distracted by the festivities, Castor and Pollux snuck away to steal back the herd. Lynceus and Idas noticed their absence, and knew what the half-brothers were up to. Lynceus and Idas left the feast in a hurry, leaving Paris alone with Helen.
While Castor and Pollux arrived at their destination, the cousins were not far behind. Castor climbed a tree to keep watch, but was easily seen by Lynceus. Idas hurled his spear at Castor, piercing the mortal twin in the heart. As he fell from the tree, he cried out to Pollux who ran over to the commotion. In his rage, Pollux clashed with Lynceus, killing him with a blow to the head.
Idas jumped upon Pollux, and thrashed him about. Just before he was set to kill the golden-haired twin, Zeus, who had been watching the brawl, hurled a thunderbolt at Idas and killed him.
As Pollux cried over his beloved brother, he begged Zeus to give his immortality to Castor so they could stay together. Upon hearing this, Zeus transformed the twins into the constellation Gemini so they can be together for all eternity.