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.
The borders of the empire evolved significantly over its existence, as it went through several cycles of decline and recovery. During the reign of Justinian I (r. 527–565), the Empire reached its greatest extent after reconquering much of the historically Roman western Mediterranean coast, including North Africa, Italy, and Rome itself, which it held for two more centuries. During the reign of Maurice (r. 582–602), the Empire's eastern frontier was expanded and the north stabilised. However, his assassination caused the Byzantine–Sasanian War of 602–628, which exhausted the empire's resources and contributed to major territorial losses during the Early Muslim conquests of the seventh century. In a matter of years the empire lost its richest provinces, Egypt and Syria, to the Arabs. During the Macedonian dynasty (10th–11th centuries), the empire again expanded and experienced the two-century long Macedonian Renaissance, which came to an end with the loss of much of Asia Minor to the Seljuk Turks after the Battle of Manzikert in 1071. This battle opened the way for the Turks to settle in Anatolia.
The empire recovered again during the Komnenian restoration, such that by the 12th century Constantinople was the largest and wealthiest European city. However, it was delivered a mortal blow during the Fourth Crusade, when Constantinople was sacked in 1204 and the territories that the empire formerly governed were divided into competing Byzantine Greek and Latin realms. Despite the eventual recovery of Constantinople in 1261, the Byzantine Empire remained only one of several small rival states in the area for the final two centuries of its existence. Its remaining territories were progressively annexed by the Ottomans over the 14th and 15th century. The Fall of Constantinople to the Ottoman Empire in 1453 finally ended the Byzantine Empire. The last of the imperial Byzantine successor states, the Empire of Trebizond, would be conquered by the Ottomans eight years later in the 1461 Siege of Trebizond.
The first use of the term "Byzantine" to label the later years of the Roman Empire was in 1557, when the German historian Hieronymus Wolf published his work Corpus Historiæ Byzantinæ, a collection of historical sources. The term comes from "Byzantium", the name of the city of Constantinople before it became Constantine's capital. This older name of the city would rarely be used from this point onward except in historical or poetic contexts. The publication in 1648 of the Byzantine du Louvre (Corpus Scriptorum Historiae Byzantinae), and in 1680 of Du Cange's Historia Byzantina further popularised the use of "Byzantine" among French authors, such as Montesquieu. However, it was not until the mid-19th century that the term came into general use in the Western world.
The Byzantine Empire was known to its inhabitants as the "Roman Empire", the "Empire of the Romans" (Latin: Imperium Romanum, Imperium Romanorum; Greek: Βασιλεία τῶν Ῥωμαίων Basileia tōn Rhōmaiōn, Ἀρχὴ τῶν Ῥωμαίων Archē tōn Rhōmaiōn), "Romania" (Latin: Romania; Greek: Ῥωμανία Rhōmania), the "Roman Republic" (Latin: Res Publica Romana; Greek: Πολιτεία τῶν Ῥωμαίων Politeia tōn Rhōmaiōn), "Graecia" (Greek: Γραικία), and also as "Rhōmais" (Greek: Ῥωμαΐς). The inhabitants called themselves Romaioi and Graikoi, and even as late as the 19th century Greeks typically referred to modern Greek as Romaika and Graikika.