Effectively the medieval Roman Empire in the East.
Founded in 330AD when Emperor Constantine transferred his capital from Rome to a custom built city near the ancient town of Byzantion. The capital was to be called Constantinople (modern day Istanbul). At its height it stretched from bits of Spain, though Italy, Africa, the Balkans, Egypt and in to Jordan/Syria/Iraq.
Byzantine bureaucracy used an extremely convoluted series of treaties, bribes, promises, marriages, hostages, blackmail, assassinations, 'lets you and him fight' suggestions and a few vicious threats to keep its neighbours from having a go at them. Thus when something is complex and interlocked it's called 'Byzantine'.
The critical blow that started the downward trend was the loss of the province of Egypt in 642ad to the totally peaceful, never agressive and not at all expansionist forces of Islam. Emperors such as Basil II (Bulgar Basher) and Alexios I stopped the rot and even expanded the Empire but it was always on a downward trend.
The empire continued in various states of power/wealth and one period of western occupation (4th Crusade 1204-1261) until 1453 when the Ottoman Turks put an end to it. They besieged and ultimately sacked Constantinople with the streets awash with the blood of its occupants (although to be fair, the Turkish regular troops did stop the looting and killing as they took control of the city ... after the place was stripped bare). Legend has the last Emperor (Constantine XI) leading a last gasp defence of the walls. Admittedly the empire was down to one city and a couple of allotments by then.
Even though the empire was Christian, Catholic nations were extremely slow to support the Byzantines resulting in the growth of Islam into the Balkans and allowing the Turks to turn the Eastern Med into an Ottoman lake for 300 years.