The Byzantine Empire, also referred to as the Eastern Roman Empire, was the continuation of the Roman Empire in the East during Late Antiquity and the Middle Ages, when its capital city was Constantinople (modern-day Istanbul, which had been founded as Byzantium). It survived the fragmentation and fall of the Western Roman Empire in the 5th century AD and continued to exist for an additional thousand years until it fell to the Ottoman Turks in 1453. During most of its existence, the empire was the most powerful economic, cultural, and military force in Europe. Both "Byzantine Empire" and "Eastern Roman Empire" are historiographical terms created after the end of the realm; its citizens continued to refer to their empire as the "Roman Empire" (, tr. ; ), or "Romania" (), and to themselves as "Romans". 

Several signal events from the 4th to 6th centuries mark the period of transition during which the Roman Empire's Greek East and Latin West divided. Constantine I (r. 324–337) reorganised the empire, made Constantinople the new capital, and legalised Christianity. Under Theodosius I (r. 379–395), Christianity became the Empire's official state religion and other religious practices were proscribed. Finally, under the reign of Heraclius (r. 610–641), the Empire's military and administration were restructured and adopted Greek for official use instead of Latin. Thus, although the Roman state continued and Roman state traditions were maintained, modern historians distinguish Byzantium from ancient Rome insofar as it was centred on Constantinople, oriented towards Greek rather than Latin culture, and characterised by Orthodox Christianity.
What is it currently called?
when its capital city was Constantinople (modern-day Istanbul, 