Achilles was the son of Peleus, king of the Myrmidons in Thessaly and an all-around hero, and the sea nymph Thetis. Zeus and Poseidon had vied for her hand until an oracle revealed she would bear a son greater than his father, whence they wisely chose to give her to someone else. According to legend, Thetis had tried to make Achilles invincible by dipping him in the river Styx, but forgot to wet the heel she held him by, leaving him vulnerable so he could be killed by a blow to that heel. Homer, however, deliberately makes no mention of this; Achilles can not be a hero if he is not at risk.
There was an oracle stating that if Achilles fought at Troy, he would die there. His mother thus hid him at the court of Lycurgus in Scyros, disguised as a woman. There he had an affair with Deidamia resulting in a child, Neoptolemus. He was found out, however, by Odysseus, who arrived disguised as a peddler with trinkets and weaponry. Achilles was marked out from the other women by admiring the wrong goods. Alternatively, he was found out by a blast of the trumpet, whence instead of cowering he grabbed a spear to ward off the attackers. From there he needed little convincing to go to Troy.
Achilles is one of the only two people described as "god-like" in the Iliad. This does not just refer to his supreme fighting ability, but also to his attitude. He shows a complete and total devotion to the excellence of his craft and, like a god, has almost no regard for life. Not his own - clearly he does not mind a swift death, so long as it is glorious - and not really of others. His anger is absolute. The humanization of Achilles by the events of the war is the main theme of the Iliad.
Shortly after the death of Hector, Achilles defeated Memnon of Ethiopia and was very soon after killed by Paris - either by an arrow to the heel, or in an older version by a knife to the back while visiting a Trojan princess. Both versions conspicuously deny the killer any sort of valor, and Achilles remains undefeated on the battlefield. His bones are mingled with those of Patroclus, and funeral games are held. A battle over his armor leads to the death of Ajax.
In the Odyssey, also by Homer, there is a passage where Odysseus sails to the underworld and converses with the shades. One of these is Achilles, who greeted as "blessed in life, blessed in death", responds that he would rather be a slave than be dead. This has been interpreted as a rejection of his warrior life, but also as indignity to his martyrdom being slighted.
The kings of Epirus claimed to be descended from Achilles through his son. Since Alexander the Great's mother was an Epiran princess, he could also claim this descent, and in many ways strived to be like his great ancestor; he is said to have visited his tomb while passing Troy. Achilles was worshipped as a sea-god in many of the Greek colonies on the Black Sea.
The first-discovered of the Trojan asteroids, named after the character described above.