In the United States, vehicle inspections are something that's left up to individual States to decide upon. I think, that in States like California & New York, they have vehicle inspections as well as engine emissions tests. But the rules & requirements will vary from State to State. A car / truck that passes the testing in one state, could fail in a State that has stricter requirements.
Im in Oklahoma. We no longer have any vehicle inspections, & have never had emissions testing. When I was younger, I can remember going to go get the testing done. It was done at basically any mechanics shop. The test was extremely simple:
1. Honk horn
2. Turn on headlights
3. Left blinker
4. Right blinker
If your car / truck could do these things, it'd pass inspection. It'd be giving an inspection sticker that allowed you to operate on public roads, for 1 year. If it failed because of a light, the mechanic would replace the light, & then you'd pass inspection.
The test didn't look at anything mechanically, or structurally.
Failing the inspection wasn't the death of a vehicle either. it'd just make it illegal for public roads. Most of the State is rural. My family had several trucks that we never drove to the nearest town, cause they didn't have an inspection sticker. They were farm trucks, in very bad shape. We kept them off public roads as much as we could. But it wasn't always possible. But since we were out in the country, there aren't cops or any sort of police force, so we'd never be stopped.
I think my State voted to get rid of the inspection process about 15 years ago or so.
I own a few trucks that'd be illegal to operate in a few states.