- For other uses, see Odyssey.
As chronicled in the Odyssey, Ulysses and his crew spent ten years traveling home after the events of the Trojan War. His vessel sailed to the Land of the Lotus Eaters, where his crew was suddenly overcome by a compunction to relax and do nothing. Ulysses survived encounters with Aeolus, cannibals, Charybdis, Cyclops, Scylla and the Sirens, challenges orchestrated by the Beings. (TOS comic: "What Fools These Mortals Be..")
In the 1990s, Khan was familiar with the Odyssey. When an unexpected visitor arrived with a connection to his mother twenty years prior, Khan considered the potential benefits. He quoted from Homer, "All strangers and beggars are from Zeus."  (TOS - The Eugenics Wars novel: The Rise and Fall of Khan Noonien Singh, Volume 2)
In 2267, the USS Enterprise encountered six Beings, including Zeus, Aeolus, Pan and Hermes. The Beings recreated Ulysses' ordeals from the Odyssey, this time challenging James T. Kirk, Leonard McCoy, and Spock to survive the confrontations. Spock was first to recognize their situations as originating in the Odyssey, but Kirk and McCoy were also familiar with it. (TOS comic: "What Fools These Mortals Be..")
In 2366, after exposure to a white hole, Geordi LaForge recreated the story of the Sirens on a holodeck. William T. Riker and Jean-Luc Picard recognized the scene as originating from the Odyssey. (TNG comic: "I Have Heard the Mermaids Singing")
In 2370, while traveling in the shuttle within the Dyson Sphere, Jean-Luc Picard felt an odd signing sound coming from a group of islands, which reminded him of the mythological Sirens. Picard thought of Odysseus and quoted from the Odyssey. (TNG novel: Dyson Sphere)
- The title page of Part One of DS9 novel: The Never-Ending Sacrifice quoted from the Odyssey: “Where shall a man find sweetness to surpass his own home and his parents? In far lands he shall not, though he find a house of gold.” 
- The contents page of VOY novel: Distant Shores quoted from the Odyssey: “Many cities of men he saw and learned their minds, many pains he suffered, heartsick on the open sea, fighting to save his life and bring his comrades home.” 
- TOS comic: "What Fools These Mortals Be.."
- TOS novel: Uhura's Song
- TOS novel: The Rift
- TOS - The Eugenics Wars novel: The Rise and Fall of Khan Noonien Singh, Volume 2
- TOS novel: Ex Machina (not named)
- TNG novel: Dark Mirror
- DS9 novel: The Never-Ending Sacrifice
- VOY novel: Distant Shores
- TTN novel: Over a Torrent Sea (not named)
- TOS novel: Burning Dreams (not named)
- TOS short story: "The Procrustean Petard" (not named)
- VOY episode: "Favorite Son" (not named)
- TNG comic: "I Have Heard the Mermaids Singing"