The Byzantine Empire

After the division of the Eastern and Western parts of Rome, the eastern remained under the rule of Constantine, the first Christian emperor of Rome. Constantine moved the capital from Rome to the city of Byzantium. He rebuilt the city and called it Constantinople, naming it after himself. This new capital city represents the end of the Roman Empire and the beginning of the Byzantine Empire. He began building monuments to create a more Christian feel in the new capital city. The first church built there by Constantinople was the church of St Eirene, and it was dedicated to Holy peace.
The fall of Rome ended the western half of the Roman Empire, and the eastern half continued as the Byzantine Empire. The empire had many different elements, a few of which were Christianity and Greek education. The Christianity developed here was the most significant cultural feature of the Byzantium Empire. It had a major influence on Orthodox Christianity, and missionary work began its spread.
The Byzantine Empire covered Greece, Balkans, Asia Minor, Syria, and Egypt. The empire looked less like a Roman empire, and had more of a Greek aspect, because the Greeks were the predominant race in the empire. Greek became the main language of the empire, replacing Latin. Also, legislation became thoroughly Greek.
The Byzantine Empire fell to Muslim invaders in 1453 because of the sack of Constantinople.
The Christianity and Greek influence in the Byzantine empire was extremely important. The spread of Orthodox Christianity lead to the adoption of a new religion still practiced in many places today. Without Constantine, and the Byzantine empire, Christianity might not have spread the way it did, and the religion would not be how it is today.

http://www.gothicmed.com/gothicmed/GothicMed/virtual-museum/greece/General/Byzantio.html
http://www.fordham.edu/halsall/byzantium/index.html
http://www.historyworld.net/wrldhis/PlainTextHistories.asp?historyid=ac59
http://www.lycos.com/info/byzantine-empire.html