The Byzantine Empire ( or Eastern Roman Empire ) was the name of the Greek part of the Roman Empire which survived into the Middle Ages . The Byzantine Empire ( or Byzantium ) was the predominantly Greek-speaking eastern part of the Roman Empire throughout Late Antiquity and the Middle Ages . Also known as the Eastern Roman Empire , the Byzantine Empire was called simply Roman Empire ( Greek : , Basileia RhÅ maiÅ n ) or Romania ( , RhÅ manÃ a ) by its inhabitants and neighbors .