We associate amphitheatres with the outdoors, and Greek theatre. There are many, all over the world, and I’ve pictured a few here. Typically, they were built as theatre in the round, for performances in the middle of two complete sets of theatres, which is what the name means.
The earliest permanent Roman amphitheatre known was built at Pompeii after a colonia of Roman veteran soldiers was established there in 80 B.C. Before this, gladiatorial contests would take place in the forum of Rome and other cities. There are many famous examples from the Roman Classical period. Being particularly associated with ancient Rome, amphitheatres were used for various types of public spectacles. In the Roman Empire, amphitheatres were nearly square, or oval in shape (the name suggests that they were thought of as resembling two theatres joined together, hence the name “amphi”-theatre), forming a complete near-circle or ellipse, and were used for spectator sports, games and displays. Romans knew amphitheaters built of stone would be stronger and more permanent than those built of wood.
There was also the hippodrome, for gladiatorial and racing events, like the Colloseum in Rome. These were immense, and much more elaborate, with areas for the participants as well as audience.
The site of the first modern Olympics, built in a style reminiscent of the Coliseum, went up in 1896 and held room for outdoor events. The games have been held in different locations ever since. The stadium was built in a modified amphitheatrical style, in tribute to their ancient nature.
The amphitheatres we build today are generally different. Our performances are presented, for the most part, for one sided viewing. There was one at my college, too, where Greek plays were presented when the weather allowed.
The Hollywood Bowl uses the amphitheatre structure, and includes a acoustical shell to enhance its musical features. Some outdoor sports facilities use the form of amphitheatre as well.