Probably the oldest fictional archetype, and certainly one of the most appealing, has been the "Lost World" model. In these humans come across some remote corner of the Earth (or in a few really out there stories whole other planets!) in which prehistory never ended, and a palaeo-environment survives. What happens in the story can vary, but inevitable a great deal of discovery and danger ensues.
The means by which prehistory endures are as numerous and diverse as the number of these stories. Geographic isolation is a key ingredient but this can be provided from the reasonable to the outright fantastic. In the reasonable category prehistory has been cut off from its extinction and the outside world by being in/on a remote island, plateau, valley, etc. The more fantastic means of preserving prehistory often are themselves a big part of the story, to explain how the humans arrive. Otherwise it would make little sense for Dinosaurs to be discovered in underground realms, frozen away in the ice, contained within a volcano, all the way on another planet...
A less ambitious version of the Lost World model is to simply have a single element of prehistory survive into the present, nestled among an otherwise normal modern environment. The majority of these tend to be about exploitation by the human discoverers and an ensuing rampage. Though in a few cases it can simply be a tale of discovery.
Probably the other "great" Palaeo Pop Culture genre is the time travel one. Rather than bring prehistory to the present, take the humans back to the past... Or in some cases the past forward to the present. This genre is pretty straight forward, but has a lot of quirky extremes and twists that have been taken.
A much older version of scientific resurrection, an equal response to technological innovation, is a radioactive infused prehistory model. These tended to involve long dormant creatures being awoken or reanimated by exposure to radioactivity (whether an explosive or just some radiation). In some of the most famous stories the creatures involved gained super powers, but this was by no means a constant. As these tales typically were a commentary on the dangers of atomic energy there tends to be a lot of destruction for humanity in the end.
Dinotopia by James Gurney
When you can't have a plausible explanation for prehistory and humans to co-exist just make belief they should. As fantasy lets you do anything you want, there's not much for me to say other than this is a very diverse genre.
Another way to bring prehistory into the present and into conflict with modern man is to have intelligent ancestors of the extinct creatures reappear. Whether they hid in a lost world, are a by-product of time travel gone wrong, or returned from outerspace these big brained remnants of the past tend to give us a fair challenge.
Through combination of the intelligent Dinosaur and fantasy genres, fiction writers sometimes want to tell their stories from the prehistoric creatures point of view. Sometimes this is simply a narrative of a normal animal, and is more like a first person documentary. At the extreme we get humanized creatures.
While this last category is more plausible than human-like Dinosaurs, I leave it to the end as it is the most fictional of the lot. In the cave people scenario humans and Dinosaurs are presented as having coexisted. Which is of course completely made up, but admittedly fun. In these man battles against the adverse odds of a savage world (in as few clothes as possible :P).