>>696457
First off, to call them Byzantines isn't really proper. They began as the Eastern half of the Roman Empire, based in Constantinople, until Theodosius gave the West to Honorius and the East to Arcadius. The East, which would become the 'Byzantine' Empire had been culturally distinct from the West for some time. The East was Hellenistic (Greek) while the West was Latin. After this split, they were simply the Eastern Roman Empire and called themselves Romans right up until Constantinople fell to the Seljuk Turks in 1453. The name 'Byzantine' comes from 'Byzantium,' which was the name of the city until Constantine administratively split the Empire and made the Eastern capital Byzantium, which he renamed as Constantinopolis (Constantine's City in Greek). The Byzantines called themselves Roman, and I think we should, too.
Now, the Eastern Empire was a bastion of Christianity throughout the Middle Ages (let us dispense with this 'Dark Ages' nonsense, which refers to a lack of documents in the West). Despite breaking with the Roman Catholic Church in 1054 (and vice versa), the Romans continued to be allies to the west against the encroaching power of the Muslim caliphates for centuries.
Throughout this era, they also continued to keep many Greek works alive long enough to be translated into Latin for the West. It was these scholars fleeing the caliphates that ushered in a renewed interest in the Classical world, and thus the Renaissance, not the Muslims.
Unfortunately, problems stemming from stagnation, bloat, internal politics, and constant incursions by Muslim barbarians eventually led to its collapse, with most of the refugees fleeing into the Slavic and other Eastern European countries.
Catholic, Protestant, and especially Orthodox all owe their freedoms to the Eastern Empire, and one of the greatest tragedies of all Christendom is that the beautiful Hagia Sophia was converted into a mosque (made all the more insulting that one of the most accepted quotes about it, so much so that it's the quote for building it in Civ 6, is that it should be made a place of 'both religions').
That's about all I know off the top of my head. Maybe a historian or well educated Orthobro could expand and correct.