The Byzantine empire which was formed from the remains of the Eastern Roman Empire continued to be a force for nearly a thousand years. It continued many Roman and Greek traditions from the past.  It's capital of Constantinople remained an important cultural center throughout.

Sources:

http://www.thelatinlibrary.com/imperialism/notes/byzantinechron.html

http://www.metmuseum.org/explore/byzantium/time.html

http://www.metmuseum.org/toah/hd/byza/hd_byza.htm