The Ludus Magnus was the largest gladiatorial training school in Rome. It was built during the reign of Domitian (81-96 AD) in the valley between the Esquilino and the Celio, an area already occupied by Republican and Augustan structures. I visited the ruins a few months ago during a nightly walk, but did not make any proper pictures of it. Only the above model is among my collection, taken in the 'Museo della Civitata Romana'. A horrible place, with only fake objects.
Next to the Ludus Magnus, three other gladiatorial training schools were located in Rome. The Ludus Mututinus was specialised in training with wild animals. The schools were supervised by Imperial procuratores. The procuratorship of the Ludus Magnus was very lucrative.
A nice Youtube filmpje shows some impressions of gladiator fights. Play the music loud!