Broadly speaking, for centuries - say from 300 BC to 500 AD - these mediterranean cultures dominated our part of the world. Everyone around the edges of them wanted in on the action, fashion, wealth - and so you get greek/roman artefacts occurring in the non-roman lands even before Rome began its rapid expansion. Even after the roman empire slowly faded away, subsequent leaders constantly aspied to be 'Roman', because the bulk of learning, writing, systems and architecture were still leftovers from way back then.
Add to this the poerful influence of Christianity, which was adoptyed by the roman empire and became a thread linking its values and influences into following societies.
So I suppose I'm saying that an entity as extensive as this, that lasted so long and reached so many geographical areas, is bound to have a lasting impact on societies that follow after, especially when (as in Europe's case) these sunsequent societies existed in a time o massive social upheaval and economic slump. Greek and Rome became kind of fantasised golden ages when everything was bigger, better, safer.