Most fiction detailing interaction between humans and dinosaurs portrays the relationship as purely antagonistic; dinos want to eat us, and we want to not get eaten. But that's not the extent of our interaction with most animals we actually deal with, is it?
This trope is another way of imagining what that interaction might look like. What if we found a use for dinosaurs? Since Everything's Better with Dinosaurs, logically, a world where dinosaurs are kept as pets, mounts, or beasts of burden is better than our own world.
Despite the name of this trope, it can also apply to any prehistoric animal.
Also see Horse of a Different Color and Cool Pet, as well as All Animals Are Dogs for what usually happens with such creatures, and Fluffy Tamer for the sort of human character who keeps these things around. Typically occurs in a One Million BC setting, a Lost World, in Medieval Prehistory, or as a result of Time Travel. A pretty severe inversion of the Prehistoric Monster trope, too, since it relies on dinosaurs being just another class of animals.
Anime and Manga
The earlier chapters of Black Cat has Madam Freesia, an aristocrat who really likes to collect rare objects, including a pet T. rex named Flora, who escapes and causes much destruction.
In Runaways, Gert has a pet raptor named Old Lace.
2000 A.D. ran with this idea by having the Cursed Earth - the post-apocalyptic wasteland between the Mega Cities of North America - infested with reborn dinosaurs. A long-running strip followed a pioneer "wagon train" leaving Judge Dredd's Mega-City One to search out an unspoilt corner of the continent in which to build a better life; they encountered both raptor packs, some of which had been "tamed" by sub-human mutant tribes as riding beasts, and by others as beasts of burden.
Elsewhere in 2000 AD, tyrannosaurs repeatedly turn on humans who try to tame them. A story arc revolved around a bull tyrannosaur with a certain sentience, who absolutely hated the humans who'd treated him sadistically.
The Valley of Gwangi. An old west rodeo makes a successful sideshow out of an eohippus, and then they find an allosaurus and try to put him in the circus. Naturally, he escapes and eats a lot of people.
The Prehysteria series of kids' movies involve pet dinosaurs.
Jurassic Park is about a failed attempt at creating a dinosaur zoo. Certain spin-off video games let you succeed, though, by focusing on the upkeep of such a park if it really worked.
In the book (although dropped from the film), one of inGen's long-term plans was to breed small dinosaurs for children to keep as pets, and make it so that they could only survive off of food produced by inGen, giving them a nice monopoly on them.
Dinotopia is a borderline example, since all the dinosaurs could talk and were basically treated like people.
Prehistoric Park is about a successful attempt at creating a dinosaur zoo. It's basically just a documentary series about the management of a zoo, but the zoo happens to be for dinosaurs.
On Primeval, Abbey kept a Coelurosauravus as a pet. His name was Rex.
The Doctor Who episode "Dinosaurs On A Spaceship" has the Doctor taming a triceratops and then riding it around the ship.
Spinoff series Torchwood gives the main protagonists a pet pteranodon.
Inverted on Dinosaurs, where the ridiculously-suburbanized dinosaurs keep pet humans.
In Warhammer, the Lizardmen ride various distinctly dinosaurian steeds into war. One such creature, the therapod-like Cold One, is also available to the Dark Elves. It's a bit of a stretch to call Cold Ones domesticated, though, as the rider needs to cover themselves in an unguent that masks their scent so the beasts won't attack them.
Warhammer 40,000's Eldar and Dark Eldar have access to Cold One-like steeds, and the Tau Empire's Great Knarloc is very much like a Tyrannosaurus rex, but they mount a big gun on its back.
The standard rules also make this definitely possible, with druids and rangers given access to various prehistoric animals as their companions. Additionally, the 3.5 supplements Frostburn and Sandstorm suggest that paladins in arctic or desert settings might use megaloceras and diprotodons, respectively, as mounts, and the book Arms and Equipment Guide offers the "axebeak" (a distinctly phorusrhacid bird) as a steed.
Module WG 6, Isle of the Ape. One of the groups of cavemen had phorusrhacids that they used as "hounds" to hunt down prey.
Pathfinder also gives druids access to dinosaurs and pterosaurs as companions, and the Kelids are a steppe nomad culture who ride domesticated mammoths.
Ironclaw and Jadeclaw have dinosaurs substitute for cows and horses. The text refers to them as "lizards," but the illustrations clearly show dinosaurs.
In Chrono Trigger, Ayla's caveman tribe keep (four-legged) pterosaurs as flying mounts while the Reptites keep Tyrannosaurs.
In World of Warcraft, trolls often ride giant raptor-like creatures, while the tauren (minotaur people) typically ride the brontotherium-like kodo.
In The Order of the Stick the Empire of Blood uses a lot of dinosaurs in their military and in their gladiator arenas.
The very first cartoon character of all time, Gertie the Dinosaur, was a saurodod who did tricks on command, and would metatextually interact with live actors. If you're having trouble picturing this, imagine the "Hello John" scene from Jurassic Park, which was a Shout-Out to this.
The Flintstones, famously. The prehistoric humans kept dinosaurs as pets and used them as industrial machines (e.g. a brontosaurus was used as a steam shovel).
In the Porky Pig short "Prehistoric Porky" cave-Porky has a pet brontosaurus named Rover.
In the Futurama episode "I Dated a Robot", Fry fulfills one of his dreams: riding a T. rex in the Jurassic Kiddie Park.
Conversed in Arthur when Arthur, Buster, and the Brain are writing a fanfic sequel to Robin Hood. Buster wants to write a scene where pirates ride an Apatosaurus into town and crush buildings. Brain points out that "dinosaurs and pirates never coexisted."
Dino-Boy. The title character had a baby brontosaurus named "Bronty" as a pet. The villains in various episodes sometimes had dinosaurs as beasts of burden, mounts, attack animals and so on.
In the Tiny Toon Adventures episode, "Rock N' Roar", Buster tried to get his soccer ball back when it fell down a hole, but instead, he picked up an egg that hatched into a dinosaur. He tries keeping him as a pet, naming him "Rover", and even raising him to be a vegetarian, but Rover's massive size made a mess of Acme Acres and Monty tried to trap him. At the end, Buster had to return Rover to the cave where he found his egg.
On the Hanna-BarberaSaturday Morning CartoonMighty Mightor, Sheera has a pet mammoth calf named Bollo. Little Rok also has a pet dodo bird, although that's a borderline example, since the dodo went extinct relatively recently. Plus, the villains of the show regularly used dinosaurs and other prehistoric animals as mounts and attack animals.
InDuckTales, Bubba the Caveduck has a pet triceratops named Tootsie.
There's a popular photoshopped image floating around the internet of Napoleon Bonaparte riding on an allosaur.
Images of Jesus riding a dinosaur or of Bible-era farmers riding triceratops are often used to advertise, or satirize, creationism.
Five hats means that five tropers think it is ready to publish.
You are saying that you think this draft is ready to be published. That means the description is not ambiguous,
it doesn't duplicate an existing trope, there are at least three examples, and the title makes sense.
Is that what you meant to do?
You are saying this draft has a ready-to-publish hat it does not deserve and you are taking it back.