The Alliance/Union universe in C. J. Cherryh's fiction is a complex, detailed future history that is the subject of most books and series she's written over the years. It's a Space Opera setting, with Faster-Than-Light Travel of the Subspace or Hyperspace type which is invented after a fair amount of sub-light exploration and colonization. All the novels take place after the FTL revolution, however. The universe is the setting for Cyteen, the Chanur Novels and the Morgaine Cycle, though the latter is only loosely connected via the back story.Not to be confused with the Union of Allied Planets from Firefly.
Artificial Gravity - notable in its absence. Ships have rotating living sections mounted on a non-rotating "frame".
Asteroid Miners - fairly common in the 'verse, but asteroid mining is the setting for Heavy Time and many of the characters of its sequel, Hellburner, are former asteroid miners.
Boarding Party - The power-armoured marines of Rimrunners, and other armed groups boarding stations and taking control in the series.
The Battlestar - The Earth Company jump carriers are examples of this, being heavily armed ships that are also serve as carriers for smaller craft.
City of Canals - the lightly connected novel Angel with the Sword and the shared-world anthologies Merovingen Nights are set in such a city.
Clones Are People Too - The Union's Azi, especially Alphas, are often treated as equals or near equals, even though their personalities are derived from tape. They can even aspire to full citizenship, much like the slaves in Ancient Rome. In 40,000 in Gehenna, an entire planet is settled with freed clones created specifically for this purpose.
Some wealthy Union citizens have "vanity clones" that are raised like ordinary children and are born with full rights.
Cloning Blues - Union, one of the factions, produces cloned soldiers and colonists in huge numbers, in an attempt to grow quickly in strength. Cyteen is set at the primary research and development centers for this cloning, and deals extensively with the ethical issues, as well as experiments to re-create individual genius talents through a combination of genetics and careful rearing, with mixed results.
Corrupt Politician: Politics, economics, and international alliances are all tied together and complicated by FTL and the individual nations that are spaceships and starships. Viking Station is a third world nation on the edge of corruption and Esperance is explicitly corrupt.
Death World - the planet Cyteen's native life is silicate and the fibers and dust it gives off is highly carcinogenic to any human that breathes it. Outside of protected enclaves, humans have to wear suits and breathing apparatus.
In general, planets with shirtsleeve environments are fairly sparse in this 'verse.
Designer Babies: Azi are really more like this than clones, some are clones granted but the whole point of them was to increase the Union's genetic diversity so most are made from donor sperm and eggs imported from earth.
Humans Through Alien Eyes - some passages in Downbelow Station are told from the point-of-view of the Downers, while the somewhat-connected Chanur series is told entirely from the point-of-view of the cat-like Hani, who spend a lot of time puzzled by the human emissary they take aboard.
Hyperspace Is a Scary Place - remaining conscious through "Jump" causes extreme psychological stress among humans, who must drug up to survive the experience sane. A small few, however, are able to stay alert without ill effects, and manage to adjust to the strange reality; they are known as "Nightwalkers". Among aliens, some are like humans, while others (such as the Hani) are simply non-functional in Jump-space, and effectively dream until the ship returns. Jump is fatal to the stshto without tranq, while the Kif remain alert and functional throughout, as, it seems, do other life-forms from their world.
Indentured Servitude: Azi have the rights of minors but they can be made citizens under certain circumstances, and their children are citizens. Considering the original point of azi was to increase the Union's genetic diversity.
Captain James Roberts is the hero of the alliance.
Satin is the only downer who can convince the only intelligent alien race we know of to tell humanity to fuck off; and we love her.
Elene Quen is the human who runs the stations, and she's no slouch.
Ariane Emory is a politician/geneticist/psychologist who plans to live forever.
Jordan Warrick is a genius, his son/clone Justin is also a genius, but not particularly legendary.
Signy Mallory: She hates Mazian.
Conrad Mazian: He refuses to accept defeat and keeps on fighting, even after he's cut loose.
Longevity Treatment: Rejuv doubles the human lifespan but causes sterility and white hair. It's made from a lifeform native to Cyteen and is the only reason the Union halted terraforming efforts.
Mêlée à Trois - the Company Wars produce, by the end, four sides: Earth and Union being the original two warring sides, while those in the middle get tired of being kicked around by both and form the Alliance. Meanwhile, the Earth Company Fleet goes rogue and is disavowed by the home planet, which starts building a new fleet under closer control.
Merchant Prince - The Alliance was created by the heads of powerful merchant clans who didn't want to be controlled either by Earth or by the newly-formed technocratic Union, so they used their wealth and power to create a new independent government headquartered at Pell which they basically control (after having fought Union to a standstill).
Raised by Natives - In Finity's End a merchant spacewoman's orphan is raised on a space station by the local humans and also the Downers from the planet below. Just as he is getting settled into that society, his mother's ship returns and forces him back into their very different society. Drama ensues.
Older than They Look - FTL travels slows down physical aging by around 25% due to a small amount of Time Dilation. So spacer teenagers look like middle school kids, twenty-somethings look like teenagers, etc.
Also there is a drug called Rejuv which is made from something native to Cyteen and freezes aging (except for turning your hair completely gray) until approximately 140, at which point your age rapidly catches up to you.
Proud Warrior Race Guy - the humans of the Alliance initially thought that the mri of The Faded Sun trilogy were this. Actually only one caste is like that; the other two thirds of the mri are non-combatant.
Settling the Frontier: In 40,000 in Gehenna, the Union sends 40,000 people, mostly Azi, off to settle a new world, the secret colony of Gehenna.
Space Marines: Fleet warships have a complement of marines. As relatively hard sci-fi their armour is minutely described and plausible as technology. The marines are key to securing assets: getting into space is exorbitantly expensive enough, so an armed starship entering a system can own it by closing with other ships and stations to secure them with the marines. The marines are able and willing to blast and cut their way to control centers, even if it means exposing parts of the station to vacuum. Life for a marine is very boring 99% of the time, being excluded belowdecks from the ship's crew. When deployed, there is the terrifying prospect their ship might suddenly need to move, with no friendly ship in-system in a decade.
Space People: Humans are divided culturally into planetsiders, stationers (space station inhabitants), and spacers. Stationers tend toward conservatism (and a welfare state), as civil unrest can lead to Explosive Decompression. Spacers' loyalty is to no place but their ship, which is often home to their entire extended family. Families are matrilineal, as the incest taboo is strictly observed and so all reproduction happens on brief, rowdy shore leaves; few spacers know who their fathers are.