The Byzantine Empire influenced the development of religion, culture, and politics in western Europe. On a religious level, the seven ecumenical councils of the Christian Church, all held before the eastern schism, were convened by emperors who ruled the eastern Greek (as opposed to western Latin) part of the Roman empire (Nicea, Chalcedon, etc. were all near Constantinople). The eastern concept of the `pentarchy` with co-equal bishops rather than a unique Pope became the model of Anglican and Lutheran ecclesiastical polity.
In culture, Greek learning and language were preserved in Byzantium after the fall of Rome in the 6th century. The tradition of ancient culture was preserved in the Byzantine and Arab worlds, and gradually transmitted back to the west from the twelfth through the sixteenth centuries, due to a combination of trade, crusades, and refugees.
Finally, the Crusades were launched in response to appeals from the Byzantine Empire for military help against Turks and Arabs.
Before 1453, Constantinople was the gateway to the Middle East for crusading armies. Byzantium was also important as a trading empire with the West, especially immediately after the fall of Rome. Byzantine pottery and metalwork was quite popular in Europe during the Middle Ages, and Byzantium was also important in the spice and silk trade with the East. Byzantine coins were regarded as very valuable with traders in Western Europe and the Middle East. Byzantine scholars also maintained studies in Greek and Roman philosophers who were considered to be pagans by the early medieval Church. This would be important during the Renaissance when Western Europe rediscovered the classics. Byzantium was also the strongest state in Christendom and may have saved Europe from being overrun by invaders from the Middle East.