(written from a Production point of view)
A Human soldier wakes up aboard the Discovery centuries after the ship has been abandoned, and develops a close relationship with the AI interface that saved him.
Alone in a V'draysh escape pod, a man known as Craft spends his time watching Betty Boop cartoons as he drifts. He loses consciousness as his life signs reach critical levels but is suddenly caught in a tractor beam. It is from the USS Discovery.
He awakens in sickbay and attempts to put on an ill-fitting jumpsuit. He then hears the voice of Zora. He believes Zora to be alive, but instead it is the Discovery's computer, which has been evolving over the past thousand years.
Craft wishes to return to his wife and child on Alcor IV, but is told by Zora that he cannot; there is only one warp-capable shuttlecraft on the ship, and after a millennium, it is likely unworkable. The Discovery cannot travel to Alcor IV because Zora is unable to disobey orders to maintain position, first given by her captain before they left the ship.
Consequently, Craft spends his time watching old movies on the bridge with Zora. Zora's favorite is the 1957 film Funny Face, starring Audrey Hepburn and Fred Astaire. The film is viewed as a holographic projection. Craft, wanting to do something nice for Zora, realizes he can dance with her through this projection, and replicates himself a coat much like Astaire's in the film. However, as they dance, he recalls his wife and child and leaves the bridge, feeling as if is being unfaithful to them. Zora tried to persuade Craft that their interactions cannot be an act of unfaithfulness because Zora is not a person – to which Craft responds, "Liar." A tear rolls down the face of Zora's holographic projection.
Zora, realizing that Craft should attempt the journey home, equips him with a spacesuit and the warp-capable shuttle and, expressing gratitude to Zora, he warps off for home to see his family, unsure if he will even make it. Zora and the Discovery continue to maintain position.
"Zora? I don’t know where you are or exactly what you are. I don't know if I'll make it home or what I'll find when I'll get there. But I know you saved my life, healed my body. You reminded me what it means to be Human..."
"Please, Craft. No poignant ironies. This is hard enough already."
"Then I'll just say goodbye."
"Craft. On your world, if we were lovers, would you tell me your name, your true name?"
"If we were lovers on my world, you would give me my true name."
"Oh, well, then I already did."
- - Craft and Zora, final dialogue between the two
- The episode's title, synopsis, and airdate were announced on 20 September 2018. 
- The title refers to Calypso (Καλυψώ), a nymph in Homer's Odyssey. She rescues the shipwrecked Odysseus and keeps him on her island for seven years, enchanting him with her singing. However, he yearns for his wife Penelope so strongly that the gods order Calypso to release him. Despite her sorrow, she complies and gives him supplies for his voyage. In addition, the name of Craft may be a further allusion to the Odyssey, as Odysseus is frequently referred to as "crafty Odysseus" (πολυμήχανος Ὀδυσσεύς).
- This is the first episode of Star Trek to not to feature any uniformed Starfleet officers. The first full length episode to not feature any uniformed Starfleet officers is the Star Trek: Picard episode "Absolute Candor".
- The date for the events of this episode has not been set due to Discovery's travel through time. This episode may mark the latest known events in Star Trek's in-universe chronology, with the possible exception of the Star Trek: Voyager episode "Living Witness".
- After Star Trek: Discovery took on a new direction with its third season by being set in a far future, the showrunners made a pledge to have future series seasons line up in canon with "Calypso",  even though there is a major canon discrepancy to iron out in order to do that: the fact that in "Calypso" (which obviously take place after season three) the ship is in its original configuration when it should be in the refit configuration with the detached nacelles. 
Links and references
- Sash Striga as Zora Holo-Dancer
"'S Wonderful"; 33rd century; Alcor system; Alcor IV; Astaire, Fred; automobile; Avery, Dick; beef; Bimbo; Boop, Betty; Calloway, Cab; carbohydrate sleeve; cheese; chess; Craft's family; cyclops owl; Earth; escape pod; evolution; flowers; flower pot; foodstuff; Funny Face; Funny Face; hammock; heavy blast armor; Hepburn, Audrey; Human; hunting; hydropulse; Koko the Clown; Long Ago, The; love; name; media files; media log; Mexico; mink; pidgin; pigeon; protein; pulse burns; pulse-rigger; Quarrel; Reach; scar; settlement; seven dwarfs; skeletons; Snow-White; sombrero; Sorrowhawk; sour cream; southwest; "St. James Infirmary Blues"; stellar cartography; Stockton, Jo; syrup; white table; taco; Taco Tuesday; tattoo; torture; true name; Tuesday; V'draysh; V'draysh escape pod; waffle; weapons rack; wind; wine
- "Calypso" at StarTrek.com, the official Star Trek website
- "Calypso" at Memory Beta, the wiki for licensed Star Trek works
- "Aye, Calpyso with Dr. Ali Mattu" at MissionLogPodcast.com, a Roddenberry Star Trek podcast
|Star Trek: Short Treks
"The Brightest Star"