Ancient Greek mystery religions?

They went to Hades, the Greek Underworld, Tartarus, if they were not worthy and Elysian Fields if they were good Greek boys and girls.

The Greek Underworld includes:

The great pit of Tartarus, which was originally the exclusive prison of the old Titan gods, but which later came to mean the dungeon home of the damned souls.

The land of the dead ruled by the god Hades, which is variously called the house or domain of Hades (domos Aidaou), Hades, Erebus, the Asphodel Fields, Stygia and Acheron .

The Islands of the Blessed or Elysian Islands ruled by Cronus (According to Pindar - other accounts differ), where the great heroes of myth resided after death.

The Elysian Fields ruled by Rhadamanthys, where the virtuous dead and initiates in the ancient Mysteries were sent to dwell.

The five rivers of Hades are Acheron (the river of sorrow), Cocytus (the river of lamentation), Phlegethon (the river of fire), Lethe (the river of forgetfulness) and Styx (the river of hate), which forms the boundary between upper and lower worlds.

The purpose of the Greek mystery religions was to ensure that their followers went to the Elysian fields, which was their version of paradise. Otherwise they would be stuck in Hades, which was a dismal place.

The River of Styx?

your Q is kinda broad.