http://www.lib.msu.edu/sowards/balkan/lecture3.html
...In 1055 Turks captured Baghdad and created the Seljuk Empire, which remained Islamic but was no longer Arab-ruled. When the Mongols destroyed the Seljuk state in the 1200s, Turkish tribes scattered West into Anatolia. One of them came to be named for Osman, its leader. They became involved in the wars of the Byzantine Empire against Bulgaria, Serbia and the Crusader states that had been set up in Greece after the sack of Constantinople in 1204. Ottoman Turkish soldiers first entered the Balkans around 1345 as Byzantine mercenaries and later returned to conquer it. They soon defeated the Bulgars and the Serbs...
...In 1444 at Varna Sultan Murad II crushed an intervening force of Hungarian, Polish, French and German crusaders. In 1453, scarcely 100 years after the Turks entered Europe, Sultan Mohammed II (known as "the Conqueror") took Constantinople by siege with an army of 100,000 and some of the world's most modern artillery. In taking the city, Mohammed II erased the last remnant of the Roman Empire and subjugated the Greek world. Symbolizing the transition, the great Church of the Holy Wisdom, Hagia Sophia, became a mosque.
After conquering Syria, Egypt, parts of the Arabian peninsula, Mesopotamia and North Africa as far as Algeria, Sultan Suleiman "the Magnificent" overran Moldavia and Bessarabia (in today's Romania) in the 1520s. At the Battle of Mohacs in 1526, his army killed 25,000 Hungarian knights and their king. The Ottoman forces reached their European high water mark in 1529 when they failed to take Vienna by siege (although they repeated the siege in 1683).