Calypso's Homeric identity begins with her father, Atlas, whom the Odyssey describes as knowing the depths of the sea and holding the pillars that separate earth and sky. Homer does not name her mother. Her home is Ogygia, a remote island whose position belongs to the geography of the poem rather than to a securely identified modern map. Around her cave grow alder, poplar and cypress; a vine hangs with grapes, four springs flow nearby, and the meadows flower with violets and parsley. Inside, Calypso sings as she works at her loom with a golden shuttle. Hermes marvels at the island's beauty when he visits. The place is secluded, but Calypso is not described as living without any attendants: the poem also mentions her serving women.

Odysseus reaches Ogygia after disaster at sea. His companions have eaten the sacred cattle of Helios, the sun god, and Zeus destroys their ship; Odysseus alone survives the loss of his crew and eventually washes ashore on Calypso's island. She receives and sustains him, but her rescue becomes prolonged detention. The Odyssey gives his stay as seven years, with his departure in the eighth. Calypso offers to make him immortal and ageless if he will remain. He nevertheless longs for Ithaca, for Penelope and for the life from which he has been separated. Her gifts cannot replace his own choice of where and with whom to live.

The poem does not present those years as an uncomplicated marriage. Odysseus spends his days on the shore, looking out over the sea and weeping for home; at night he shares Calypso's cave unwillingly. Athena raises his suffering before Zeus, who directs Hermes to secure his release. The messenger reaches Ogygia and finds Calypso at her loom. She recognises and welcomes him, offering the food and drink of the gods before asking why he has come. His answer turns the beautiful island into the setting for a confrontation about the hero's freedom: Zeus has ordered that Odysseus must no longer be kept there.

Calypso protests against the command. She accuses the gods of jealousy when goddesses take mortal lovers, recalling other divine-mortal relationships as examples of the unequal treatment she perceives. She also reminds Hermes that she saved Odysseus when he arrived without companions, and that she has offered him life without ageing. These are Calypso's arguments within the poem, not an erasure of the man's unwillingness to stay. She accepts Zeus's authority and agrees to help him depart, although she has no ship and crew to send with him. When she tells Odysseus, he is initially suspicious rather than simply delighted: the proposal to cross a dangerous sea on a raft makes him fear another deception. He asks for an oath that she means him no further harm, and she gives it.

Calypso then asks whether he would still choose home if he knew the suffering ahead, contrasting mortal Penelope with her own immortal beauty. Odysseus acknowledges the difference but insists that he longs to return. The next morning she supplies an axe and an adze and leads him to timber suitable for his vessel. He cuts and works the wood, while she brings tools and cloth for the sail. The raft is Odysseus's construction, made possible by her assistance, rather than a craft she builds with her own hands. When it is ready, she provides clothing, wine, water and food and sends a favourable wind. Her final actions help him leave the captivity she had previously maintained, without undoing the years he has spent wishing to go.

Later writers give the story different lengths and different family endings. The closing genealogy of Hesiod's Theogony names Nausithous and Nausinous as sons of Calypso and Odysseus, without calling them twins. Apollodorus's Epitome gives a five-year stay and names Latinus as their son, whereas Hyginus's Fabulae 125 gives one year. An isolated fragment attributed to the lost Telegony and preserved through Eustathius names Telegonus or Teledamus in this connection; it should not be presented as Proclus's account of two sons, or confused without explanation with the better-known Telegonus born to Circe. Hyginus separately includes Calypso among women said to have killed themselves for love in Fabulae 243. Homer supplies none of these later endings for her: after helping Odysseus sail away, she passes out of his homecoming narrative.