Inspection requirements are set by the US states, with additional requirements sometimes imposed by counties, cities, and municipalities.
Vehicle inspections generally fall into three categories:
Emissions inspections (also known as smog checks) are generally required in areas with high population density that are prone to smog
Safety inspections vary from state to state. Some states perform simple visual checks (lights, horn, signals), while others require more extensive inspections (brake and seatbelt functionality, etc.).
VIN inspections help control the registration of stolen vehicles. Some states require a state official to physically verify that the VIN on the chassis matches the VIN on the application for registration and title. This check is most common for vehicles purchased in another state.