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 Wars
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