The Flavian Amphitheater (the original name) was inaugurated in the year 80 AD after 8 years of hard work and financed by the treasures from the Siege of Jurusalem (70AD) by Titus. After two years the Emperor Domitian had the underground room digged under the arena to be used as the backstage where the fierce beasts woukd suddenly be lifted from. Its corridors and rooms were used for the preparation of the shows, the location where to keep costumes and settings for the Romans' entertainment.
The arena could be filled with water (before the underground was digged) to organize sea battles (naumachiae) and reenact important past events thanks to the aqueduct built by Nero for his Golden House.
Below You can see those sections most visitors do not see since a special permit is required, plus a view from the third level where women sat separated from men.