Eagles and thunder-gods often appear together, but in Greek myth the eagle was Zeus’ accomplice as well as his emblem. It stole the beautiful youth Ganymede from his fields and carried him to Olympos to be Zeus’ cupbearer. (Ganymede is also in the heavens, as the constellation Aquarius.)
The eagle also carried out Zeus’ punishment of Prometheus, who stole fire to give to the humans. Zeus had him chained to a cliff face, and the eagle came every day and tore out his liver. Hercules rescued Prometheus as part of his 11th Labour and killed the eagle. Zeus then put it in the sky to reward its faithful service.
The Eagle features among the Hercules family of constellations, by the way, which include large asterisms like Ophiuchus the Snake-Handler as well as tiny ones like Ara, the Altar.