Hades - the name for the Theoi Underworld, not to be confused with Hades, its ruler, is a cold and desolate place. Fields of grey and white grass or rocky fields cover this land, dark rivers channeling Souls towards an eternal greyness.
To enter Hades, one needs to die on Greek lands, and be taken to one of the entrances either by Hermes or his servants, or if the death was peaceful, Thanatos, primordial Titan of Sheol allied with the Gods. Then, to cross the river Styx, one needs to pay Charon, the ferryman of the dead, with a silver coin. Then, the gates of Hades are protected by the three-headed dog Cerberus, who lets few Souls in, and none out. The Soul is then judged by Minos, Judge of the Underworld, who decides which level of afterlife the Soul deserves.
The most worthy Souls are rewarded with entering the Elysium Fields, a bountiful paradise situated in the Godrealm of Olympus - not unlike the Norse Valhalla. When offered with the choice to enter the Elysium Fields, one can choose to refuse, and be reincarnated instead. If a Soul achieves the Elysium Fields three times in succession, they are allowed in the Isles of the Blessed, an eternal perfect paradise.
However, most Souls end up in Asphodel Meadows, a vast area where multiple rivers flow, all of which turn those who drink from them mad in some way - the Lethe makes one forget, the Styx fills one with hatred, the Acheron is the river of pain, the Cocytus is the river of wailing, while the Phlagethon, river of fire, leads to Tartarus itself.
Tartarus is where the Titans and the worst creatures to ever exist are burried, alongside the most vile mortals. Only a handful of mortals have comitted crimes dire enough to be thrown in the depths of Tartarus.