The Roman (Byzantine) Empire had lost two-thirds of its territory to the Islamic Caliphate during the eighth and ninth centuries. After a brief recovery in the late tenth century, the eleventh century saw the arrival of the Seljuk Turks into Anatolia (modern-day Turkey, so you can see where this is going.) The Turks were nomadic people from the Eurasian steppe, who specialized in horsemanship and archery. The heavily armored Romans had trouble keeping up with their quick maneuvering. In 1071, the Romans lost a 20,000-man army to the Turks at the Battle of Manzikert; Emperor Romanos IV Diogenes was captured and the Romans effectively lost control over their western border.
In 1095, Emperor Alexios Komnenos asked Pope Urban IV for military aid against the Turks, hoping to recapture the city of Nicaea, which was important as the site of the first church council and very close to Constantinople. Western Europe responded with the First Crusade, which not only recaptured all of Anatolia, but continued south, reasserting Christian control of Syria, culminating with the recapture of Jerusalem in 1099.
Although the European knights who took these lands had technically sworn allegiance to the Byzantine Emperor, they really ruled the area themselves as the Crusader States.
A Second Crusade to retake Edessa in 1147 was a failure, and Islamic armies under Saladin retook the whole area in 1187. This prompted the Third Crusade in 1189, famously under King Richard "Lionheart" of England, but the crusaders once again failed to take Jerusalem.
The Fourth Crusade, which was supposed to go to Egypt to take Alexandria, instead wound up sacking Constantinople in 1204. This, more than anything, solidified the East-West schism and delivered the fatal blow to Roman power in the East.
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