Odysseus travels to the River of Ocean in the land of the Cimmerians. There he pours libations and performs sacrifices as Circe earlier instructs him to do to attract the souls of the dead. The first to appear is that of Elpenor, the crewman who broke his neck falling from Circe’s roof. He begs Odysseus to return to Circe’s island and give his body a proper burial. Odysseus then speaks with the Theban prophet Tiresias, who reveals that Poseidon is punishing the Achaeans for blinding his son Polyphemus. He foretells Odysseus’s fate—that he will return home, reclaim his wife and palace from the wretched suitors, and then make another trip to a distant land to appease Poseidon. He warns Odysseus not to touch the flocks of the Sun when he reaches the land of Thrinacia; otherwise, he won’t return home without suffering much more hardship and losing all of his crew. When Tiresias departs, Odysseus calls other spirits toward him. He speaks with his mother, Anticleia, who updates him on the affairs of Ithaca and relates how she died of grief waiting for his return. He then meets the spirits of various famous men and heroes and hears the stories of their lives and deaths.
Odysseus now cuts short the tale and asks his Phaeacian hosts to allow him to sleep, but the king and queen urge him to continue, asking if he met any of the Greeks who fell at Troy in Hades. He relates his encounters there: he meets Agamemnon, who tells him of his murder at the hands of his wife, Clytemnestra. Next he meets Achilles, who asks about his son, Neoptolemus. Odysseus then tries to speak with Ajax, an Achaean who killed himself after he lost a contest with Odysseus over the arms of Achilles, but Ajax refuses to speak and slips away. He sees Heracles, King Minos, the hunter Orion, and others. He witnesses the punishment of Sisyphus, struggling eternally to push a boulder over a hill only to have it roll back down whenever it reaches the top. He then sees Tantalus, agonized by hunger and thirst. Tantalus sits in a pool of water overhung by bunches of grapes, but whenever he reaches for the grapes, they rise out of grasp, and whenever he bends down to drink, the water sinks out of reach. Odysseus soon finds himself mobbed by souls wishing to ask about their relatives in the world above. He becomes frightened, runs back to his ship, and immediately sails away.
This is the Nekuia or Book of the Dead.
In the Homeric understanding, the deceased do not have a proper, full afterlife in a heaven or a hell - they experience a joyless half-existence as wraiths in a shadowy realm of the dead. It is a bit like the primitive Israelite conception of sheol.
Odysseus interviews a succession of heroines and heroes - heroines first. We are reminded again of the story of Agamemnon and his death when Odysseus speaks with him. Odysseus' talk with Akhilleus is particularly striking. In the Iliad, Akhilleus famously said that he had chosen to win fame (kleos) on the battlefield instead of having a journey home (nostos) and a long life. It looks like he's now having second thoughts:
"No, do not speak well to me of death, glorious Odysseus.Despite his apparent indifference to his own continuing kleos, Akhilleus still appears to have concern for his father's honour (timé) in the land of the living.
I would prefer to live on earth as another man's serf,
the serf of a landless man, who has a scant livelihood,
than to rule over all of the decayed dead."
Odysseus' mother Antikleia tells him that she died of grief at his absence, and that his father is going the same way. However, Teiresias lets Odysseus know that he will indeed enjoy a "honey-sweet homecoming" (noston meliédea). He also makes an enigmatic prophecy that Odysseus, after getting back to Ithaka, will have to make another journey to propitiate Poseidon's anger.
It is often said that the last part of Odysseus' visions - in which he actually seems to be walking around inside the underworld - is a later interpolation into the poem (lines 568-627). Only in this part of the Book do we seem to see a later conception of post mortem rewards and punishments.