In 330 BC stone seats were added (some think there were wooden seats up until this time), and the remains of these are the ones you see today. It was able to seat up to 17,000 people. The seats in the first row were reserved for dignitaries, and you can still see some of the reliefs.
The actual stage building was also developed over the centuries. Here you can see reliefs which show the legend of Dionysus. These are also from Roman times.
The Roman emperor Hadrian (who seems to pop up everywhere in the ancient world) had a special seat reserved at the Theatre of Dionysus just for himself. This is an indication of the high regard the Romans had for the ancient Greeks and their achievements.