The play is based on the myth of Prometheus, a titan who gave the gift of fire to mortals and was punished by the god Zeus for this. Prometheus (whose name means 'foresight') possessed prophetic knowledge of the person who would one day overthrow Zeus, but refused to divulge this knowledge.
The play is composed almost entirely of speeches and contains little action. Cratos (might), Bia (violence), and Hephaestus chain Prometheus to a mountain in the Caucasus and then depart. The daughters of Okeanos, who make up the chorus, appear and attempt to comfort Prometheus by conversing with him. Okeanos himself, a friend, arrives and warms Prometheus not to arouse the further wrath of Zeus by boasting of the god's future overthrow. Io, a maiden whom Zeus pursued, and who has been changed into a cow by Zeus to save her from the wrath of Hera, appears, and Prometheus gives her knowledge of her own future. Finally, Hermes is sent down by the angered Zeus to demand that Prometheus tell him who it is that threatens to overthrow the king of the gods.
Throughout the play, Prometheus remains defiant, identifying Zeus as a tyrant and criminal. He contrasts his own concern and sacrifice for the race of mortal men with Zeus's desire to destroy them. This treatment of Zeus is quite different from his treatment in other Attic plays, and is one sign that Aeschylus, who described Zeus as 'father of gods and man', had no part in this. It is possible that the play was written as a political allegory.
Prometheus Bound was not highly regarded among Greek plays until the early 19th century, when romantic writers came to identify with the defiant Prometheus. Lord Byron became attached to this play in childhood, and claimed that it worked its way into everything he wrote. Percy Bysshe Shelley wrote Prometheus Unbound, which used some of the materials of the play as a vehicle for Shelley's own vision.