The Eastern Roman empire, founded by the emperor Constantine I in 330 CE. Constantine (r. 306–337 CE) transferred the imperial capital from Rome to the port city of Byzantion, located on the eastern edge of Europe at an important hub of east–west trade. He renamed the city Constantinople (it is present-day Istanbul, Türkiye). Constantine threw his support behind the Christian religion. As a result, Christianity gradually supplanted the Greco-Roman gods in the empire. The Byzantine Empire survived until 1453, when the Ottomans captured Constantinople .

Byzantine art is conventionally divided into three periods: Early Byzantine (ca. 330–843), Middle Byzantine (ca. 843–1204), and Late Byzantine (ca. 1261–1453). The Early Byzantine period witnessed an empire-wide boom in church building under Justinian I (r. 527–565). Justinian’s church of Hagia Sophia in Constantinople is one of the greatest architectural achievements of any age. Justinian also commissioned churches and fortifications outside of the capital, including Saint Catherine’s Monastery in the Sinai peninsula of Egypt. The Transfiguration mosaic in the Church of St. Catherine there and the wall mosaics of the Church of San Vitale in Ravenna, Italy, are the finest surviving examples of Early Byzantine mosaic art. Other high points of Early Byzanitne art are the illuminated manuscript known as the Vienna Genesis (National Library, Vienna) and the Archangel Ivory (British Museum, London).

The Middle Byzantine period followed a period of crisis, the Iconoclastic Controversy, when the use of religious images was hotly contested. The centralized cross-in-square plan for church architecture developed in this period; outstanding examples survive at Hosios Loukas and Daphni in Greece. Wealthy patrons commissioned carved ivories such as the Harbaville Tryptich (Musée du Louvre, Paris). The art of enamel also flourished, as demonstrated by surviving masterpieces: the Fieschi Morgan Reliquary (Metropolitan Museum of Art, New York) and the Monomachos Crown (Hungarian National Museum, Budapest). The Paris Psalter, an illuminated manuscript of the tenth century (Bibliothèque nationale, Paris), is often cited as evidence for a renewal of interest in classical style during the Macedonian dynasty (876–1056).

Between 1204 and 1261 the Empire suffered another crisis: the Latin Occupation. Crusaders from Western Europe captured Constantinople in 1204. The city was retaken in 1261 by Michael VIII Palaiologos (r. 1261–1282), and although the territory, wealth and power of the empire had shrunk, the arts continued to flourish under the Palaiologans, the last Byzantine dynasty. Icons painted in tempera on wood panels were produced in increasing numbers in the Late Byzantine period. Portable icons were also crafted in the new technique of miniature mosaic. Fresco painting was used in the decoration of churches, most notably in the Chora Church in Constantinople (ca. 1316–1321).

Although the fall of Constantinople ended the Byzantine Empire, Byzantine art lived on after 1453. The emerging Russian Empire carried on as the heir of Byzantium, with Orthodox churches and icons created in a Russo-Byzantine style. In Italy the Italo-Byzantine style (or maniera greca) also borrowed heavily from Byzantine traditions. Web resources here, here and here.