Generally speaking, Greek theatre and plays have had a lasting impact on Western drama and culture. It is in ancient Greece that the origin of western theatre is to be found. It developed from a state festival in Athens, honoring the god Dionysus. The Athenian city-state exported the festival to its numerous allies in order to promote a common identity.
As for honoured actors, I know several distinguished Russian headliners, for example, Nickolay Tsiskaridze, Ilze Liepa, Mihail Dyakov. All of them are the Bolshoi theatre big-name actors.