Ancient Greek religion was Polytheistic. The Ancient Greeks worshipped twelve gods known as the Olympians. They are, Zeus god of the sky, Poseidon god of the sea, Hades, god of the underworld, Hestia goddess of the hearth, Demeter goddess of spring, Hera goddess of motherhood and family, Athena goddess of wisdom, Artemis goddess of the hunt, Apollo god of music and prophecy, Ares god of war, Hephaestus god of crafting, Aphrodite goddess of beauty, and Hermes god of travelers and thieves.
Elysium was the part of the Underworld for heroes. There you could party in eternal paradise forever.
The Fields of Asphodel were where the average everyday people were sent. The farmers, the cooks, and the peasants were sent here. You are forever going to stand around and slowly fade away.
The Fields of Punishment were reserved for people who did evil during their lives and are forced to experience eternal punishments for their crimes.
Tartarus is not only a deity but the name of a place even lower than the Underworld where the evil monsters, Titans, and Giants are imprisoned. All of the Olympians sworn enemies were imprisoned in Tartarus.