In Greek Mythology, Hell had 4 rivers, the Phlegeton, Styx, Cocytus and Lethe.
Phlegeton had a particular aspect; it had flowing fire instead of water.
Styx is the river which Charon uses to transport the soul of the dead to the underworld against a payment.
Cocytus is a river which is filled with with the tears of the thieves, murderers and other bad people. Many souls walk along the banks of Cocytus to search for the underworld because they did not received funerals but will not reach it until the judges of Hell have decided about their fate.
When the souls are being re-incarnated, they drink the water of river Lethe to forget about their previous life and the moments they passed in Hell.