Phaethon never made it to the sun; his chariot was as strong as his determination, but the horses used to pull the chariot were too feisty and they stampeded. Cycnus, Phaethon's close friend, begged Jupiter, god of the skies, to help Phaethon. Jupiter duly responded by sending a firebolt of lightning across the skies to stop the frenzied horses, and this worked; the horses stopped dead in their tracks.
Cycnus dives to recover the body of Phaethon
Sadly, they halted so abruptly that Phaethon was catapulted from the chariot and as he streaked across the sky like a shooting star, he died. Phaethon's body burnt up leaving sparks as it flew (these sparks are now seen as the Milky Way) and his charred remains crashed into the river Eridanus.
His friend Cycnus dove into the river repeatedly to recover the body, but to no avail. Jupiter felt sorry for Cycnus and changed him into a swan to make his search easier. Since that day, the swan has been known as Cygnus (Latin for 'swan') and if you look in the northern sky at night you can see him still diving.
There are several other stories regarding this constellation. The brightest star is Deneb in the swan's tail, 1,800 light years away and one of the vertices of the Summer Triangle asterism.
The other two stars of this triangle are Vega and Altair. In Chinese and Japanese mythology, the stream of stars (amanogawa) from Daneb (α) to Albireo (β) at the swan's beak separates two lovers represented by the stars Vega and Altair, who are permitted to meet just once a year. This special day is called tanabata in Japan, and is held on the seventh day of the seventh month.
Another space-travelling chariot story here
Star cluster Vega represents the kimono-cloth weaver named Orihime in Japanese and Niu Lang in Chinese.
Star cluster Altair represents the cow herder named Hikoboshi in Japanese and Zhi Nu in Chinese.