djogloc02 said:
What I wanted to know was what made they lost their lands on Europe.
In Europe? Well, I guess we could say that started in the 6th century or so - the Lombards (and the various other Pannonian tribes that went along with them) invaded and occupied much of Byzantine Italy, and only Southern Italy remained Byzantine for a longer period of time after that, until the Normans conquered it in the 11th century, IIRC.
In the Balkans, the Byzantines lost much of their lands also during the second half of the 6th and early 7th centuries to the incoming hordes of Slavs. Of course, those lands had been invaded on and off for at least 3 centuries by then (first the Goths (a very destructive invasion of theirs), then the Huns, Goths again, Bulgars, Avars, Slavs, Avars+Bulgars+Slavs (again very destructive) and finally the Slavs settled down, all the way down south to the Pellopponesos in Greece)), but the Slavs were the first to actually settle in those lands and separate them from the Empire for good.
Spain, as was mentioned, was lost to the Vandals earlier on.
And I'm not sure when did they lose their holdings on the Crimean Peninsula, I think it was after the Fourth Crusade.
Oh, or if you mean when did they finally lost all of their European (and other) lands - during the Ottoman invasion (14th-15th century), when the Byzantine Empire and the other Balkan states were fully conquered and, unlike them, Byzantium was never reborn.