- Run the emulator one frame normally, using real polled input. Somehow snapshot the state.
- Then, run the emulator n frames (usually just one) with the same input. Present the video + audio from the last frame.
- Synchronize. (Some emulators can get very fancy; instead of just waiting for vsync, they'll also delay until the end of the window minus estimated processing time, to poll input at the last possible moment.)
- Roll back to the saved snapshot. (I believe you can also optimize if you know the inputs really didn't change, avoiding a lot of rollbacks at the cost of less predictable frame times.)
The main reason this is even a good idea is because most games will have some of their own processing latency by design, so jumping a frame or two ahead usually doesn't have any noticeable side-effects. This is a pretty cool idea since obviously modern computers with LCD screens have a lot more latency basically everywhere versus older simpler machines connected to CRTs.
Unfortunately, this sort of approach only works when your emulator's state is small enough and fast enough to restore.
I actually have been dying to experiment with designing an emulator to have fast incremental snapshots from the ground up to see if you could manage to make this feasible for more modern consoles. You could, for example, track dirty memory pages with userfaultfd/MEM_WRITE_WATCH, and design structures like JIT caches to be able to handle rewinding without having to drop the entire cache. I'm actually not sure that all emulators clear their caches upon loading state, but you know, more generally, I would like to know how fast and small you could get save states to be if you were designing for that from the ground up.