Warning: SPOILERS for Star Trek: Discovery season 3, episode 4, "Forget Me Not".
Star Trek: Discovery's the Burn brought back the need for Generation Ships in the 32nd century, a concept which was first seen in Star Trek: The Original Series. The Burn was a galactic cataclysm involving the destruction of dilithium that happened sometime in the 31st century; without the crucial element to power thousands of starships, the United Federation of Planets collapsed over a hundred years before Commander Michael Burnham (Sonequa Martin-Green) time-traveled to 3188 and was joined by the U.S.S. Discovery a year later.
Generation Ships (or Generational Ships) are starships used by species who lack warp capability but attempt long-distance travel across deep space. The crews of these vessels expect to spend a lifetime in transit and their children or grandchildren would be the ones who complete their voyage. Captain James T. Kirk's (William Shatner) Starship Enterprise encountered a couple of Generation Ships in TOS; the transports come in all shapes and sizes, including an asteroid ship called the Yonada used by a humanoid race named the Fabrini. On Star Trek: Voyager, the idea was even floated that the U.S.S. Voyager might have to resort to becoming a Generational Ship after they got stranded in the Delta Quadrant and faced a journey back to Earth that was expected to last over 70 years, and they encountered other Generation Ships as well. Plus, in Star Trek: Enterprise season 3, the NX-01 Enterprise encountered a doppelganger Enterprise that was tossed backward in time and became a Generational Ship crewed by the children and grandchildren of Captain Jonathan Archer (Scott Bakula), T'Pol (Jolene Blalock), Trip Tucker (Connor Trinneer) and others.
The bleak realities of Star Trek: Discovery's 32nd-century future has brought back the need for Generation Ships. Because of the Burn, most of the dilithium in the galaxy is gone or under private control by cabals like the alliance between the Orions and Andorians so there are few warp-capable starships in operation. Other planets, like United Earth, are stockpiling their dilithium supplies and have sealed themselves off from the rest of the galaxy. Yet many species still have the need for interstellar travel and, without reliable warp drive, the only option is to attempt voyages across the vastness of space using only impulse engines. That requires starships becoming Generational Ships, with its passengers knowing full-well that they will likely never see their destination and their progeny will have to complete their journeys.
In Star Trek: Discovery season 3, episode 4, "Forget Me Not", it's revealed that Adira (Blu del Barrio) and Gray Tal (Ian Alexander) were aboard a Generation Ship traveling to the new location of Federation headquarters two years before the U.S.S. Discovery arrived in the future. However, the Generation Ship was mysteriously attacked, killing Gray and necessitating the Tal symbiont be placed in Adira as its host, even though she is human and not Trill.
However, the 24th-century Star Trek: The Next Generation era also has Generation Ships since, despite Starfleet being in its heyday, there are numerous pre-warp civilizations attempting intergalactic travel. In Star Trek: Lower Decks episode 4, "Moist Vessel", the U.S.S. Cerritos and U.S.S. Merced had to tow a derelict Generation Ship to a starbase. The inhabitants of the Generation Ship were long dead and mummified, but the vessel contained a dangerous terraforming emulsion that got loose, destroyed the Merced, and nearly did the same to the Cerritos.
No doubt, there are many other Generation Ships navigating the galaxy in the 32nd century, with an unknown number of beings whose entire lives are now spent living on a starship in hopes of traversing distances that warp drive would have made possible in a fraction of the time. However, why Adira and Gray's Generation Ship was attacked and by whom are questions Star Trek: Discovery season 3 needs to address.