What is the name of the fiery river in the underworld visited by Odysseus?

The fiery river in the Underworld visited by Odysseus is Pyriphlegethon.

In Homer’s Odyssey, Pyriphlegethon is one of the Underworld’s rivers. Its name combines Greek words associated with fire and burning, giving it the sense of “fire-flaming” or “blazing with fire.” Homer describes it in connection with the river Acheron and the nearby Cocytus as Odysseus performs the rites needed to summon the dead.

Odysseus does not explore the Underworld like a modern traveler moving through a physical kingdom. Circe directs him to the far western boundary of Oceanus, where he digs a ritual trench, pours libations, and sacrifices animals. The shades gather so he can question Tiresias and learn how to return safely to Ithaca.

Lethe is associated with forgetfulness, Styx with oaths and divine boundaries, and Cocytus with lamentation. Later writers, especially Plato and Virgil, expand and sometimes alter the geography and symbolism of the infernal rivers, so their depictions should not be treated as identical to Homer’s.