The Byzantine Empire
Byzantium in the Eleventh Century
The tenth century was a glorious time in the Empire, with strong rulers and general prosperity, but the eleventh century saw chaos and loss. A convenient place to mark the turning point is the death of Emperor Basil II in 1025. After his death, rival families contended for control, with the two leading rivals being the Ducas and the Comneni. Both sides made extravagant grants of privileges and power to anyone whom they thought might be of help, decreasing the ability of the emperor to govern. The army became almost independent, creating further disruptions.
Political disorder invites predators, and the Empire by mid-century found formidable enemies rising against it: the Slavs to the north, the Normans to the west, and the Turks from the east. The emperors were able to fend off the first two, but in 1071 the Turks inflicted a catastrophic defeat on the Byzantines at 
Manzikert. The Emperor Romanus Diogenes was captured, most of Asia Minor was lost, and the Empire fell into ten years of civil war.
Everyone invaded. The Empire lost its frontier along the Danube River to the Slavs, and it lost Italy to the Normans. Syria was gone, and many Greek islands soon followed. By the time Alexius Comnenus emerged as undisputed emperor in 1081, he had little more than Constantinople itself. He spent the rest of his reign trying to regain what had been lost since the days of Basil II.
This was the situation in Byzantium at the time of the First Crusade. Alexius had dealt successfully with the Petchnegs and the Normans, and now wanted to make some progress against the Turks. He had Vikings as his personal bodyguard (the famous Varangian Guard), and he had had more experience than he cared for with the Normans (who had repeatedly invaded his lands). So he knew the value of the Latin knights. But he wanted them firmly in his service, to help him recover Antioch and Nicaea and Iconium and the other lands so recently lost to the Turks.