This is my view of the whole "Ancient Greeks", and I am shoveling everything Greek in there:

Because of conquests by Alexander the Great of Macedonia, Hellenistic civilization flourished from Central Asia to the western end of the Mediterranean Sea.

Classical Greek culture, especially philosophy, had a powerful influence on the Roman Empire, which carried a version of it to many parts of the Mediterranean Basin and Europe. For this reason Classical Greece is generally considered to be the seminal culture which provided the foundation of modern Western culture and is considered the cradle of Western civilization.

So to summarize it: Conquerors of the ancient world are emulated by successive conquerors.