The amphitheatre at Pompeii is the oldest surviving Roman amphitheatre in existence, built around 70 BC — predating the Colosseum in Rome by 140 years. It could hold 20,000 spectators — essentially the entire population of the city, which gives a sense of how central gladiatorial combat was to Pompeian public life. The amphitheatre is elliptical, sunk into the ground to reduce the height of the surrounding walls, and the seating terraces are mostly intact.
Walk around the exterior first: the arched entrances, the vaulted staircases, and the rope-holes in the top course of stonework that held the canvas awning (velarium) that protected spectators from the sun. Then descend into the arena itself. The experience of standing on the arena floor and looking up at the empty stone seating is haunting in a way that the busier parts of the site are not.