The Colosseum–whose formal monument name is Flavian Amphitheatre–is one of Rome's most visited and recognizable landmarks. From the recently restored third tier, now open to the public, visitors enjoy an extraordinary view over the inner space of the structure, and of the surrounding archeological site. The other vast space made available to visitors after the recent restoration is the underground level. The descent into the hypogeum takes us to the area beneath the arena floor where the wild beasts caught in the remotest corners of the Empire were kept, and where the gladiators about to face them prepared for the fight.
Are you planning on visiting the Colosseum? Here's some very useful information
For guided visits with knowledgable, interesting docents, I suggest Context Travel