Here are several videos that track the rise and fall of the Byzantine Empire.
The first video, by S&F Production, offers an overall look at Byzantium between the years 395 and 1453.
Costas Melas has created five videos that focus on the Byzantium during the years 324-610, 610-867, 867-1057, 1057-1204, and 1204-1453.
EmperorTigerstar has also created a couple of videos. The first tracks the Russo-Byzantine War of 941
The second looks the fall of Constantinople in 1453
Finally, profxyzful created this video showing the changing borders of Byzantium along the Near East between the years 590-1460