After the sixth century, there was massive migration from central Asia because of overpopulation in a fragile pastoral economy. One group who migrated were the Oguz Turks, who in the tenth century embraced Islam. In a tribal split one branch led by the descendants of the khan Seljuk moved west and joined with the Abbasid caliphs[spiritual leader of Islam] of Baghdad.
In 1055 a Seljuk khan, Tugrul Bey occupied Baghdad and force the caliph there to recognize him as sultan in Persia and Mesopotamia. With the expansion of the Byzantine Empire, territory of Christian Armenians and Greeks was invaded; because these two Christian groups were at odds with each other, they were unable to defend themselves and, after the Armenian culture formed on its own in the fifth century, it fell to the Seljuks under Osman Bey in the late eleventh century. Eventually, the Byzantine officials of Anatolia of which the Seljuks had won control were replaced the a new elite that was Turkish and Muslim. Consequently, conversion to Islam progressed steadily thereafter by the imposition of customs and intermarriage. Later, in 1453, Constantinople was conquered by Mehmed II and the Ottoman state was changed into a contiguous transcontinental empire.
With the conquest of Constantinople, the emergence of Ottoman as an empire happened under Mehmed n al-Fatih the Conqueror. This conquest in 1453 removed the last major barrier to expansion into northern Anatolia, a conquest which enabled the Ottomans to dominate the Straits and the southern shore of the Black Sea.The reign of Suleiman I from 1520-1566 saw the Ottoman Empire reach its apex as its political, military, and economic power was superior. Suleiman himself personally led military campaigns that resulted in the conquest of Christian Serbia, the Greek island of Rhodes, and most of Hungary. These campaigns ended with the Vienna Siege in 1529. According to historian Toynbee,
The failure of the first [siege of Vienna] brought to a standstill the tide of Ottoman conquest which had been flooding up the Danube Valley for a century past.
The Crusades, begun by Pope Urban in 1095 resulted in the sacking of Constantinople in 1453 during the Fourth Crusade because the Christian church could not reconcile the East-West Schism mentioned earlier that led to the weakening and eventual fall to the Ottomans of the Byzantine Empire. So, there was a war between Christians and Muslims with the conflict between the Byzantine Empire and the Ottoman Empire, which effected conversion to Islam with its conquests.