What happened to the dead people when they traveled river Styx?

The river Styx is a famous river in Greek mythology that separates the world of the living from the underworld, known as the realm of Hades. The dead did not travel over the Styx, but rather the river Acheron, which was one of the five legendary rivers of the Greek underworld through which the souls of the deceased had to pass.

Once travelers crossed the River Acheron, they would arrive at the gates of Hades, where the three-headed dog Cerberus would guard the entrance and prevent any living person from entering and any dead person from leaving.