The Ottoman Empire lasted from 1299 to 1922. With Istanbul (Constantinople) as its capital city, in many respects it was an Islamic successor to the Eastern Roman (Byzantine) Empire.
The Ottoman Empire in theory tolerated Christians and Jews. Mehmed II allowed the local Christians to stay in Constantinople after conquering the city in 1453, and in 1461 Sultan Mehmed II established the Armenian Patriarchate of Constantinople. Previously, they were seen as heretical.
In terms of policy matters, the empire's relationship with the Greek Orthodox Church was largely peaceful. In practice, however, Christians faced discrimination in every level of society.
Voluntary conversion to Islam was often greeted by Ottoman authorities, and it was no secret that Muslim authorities perceived Islam as a higher form of belief. In addition to this, conversation to Islam meant that those who were formerly Christians did not have to worry about paying the Jizya, a tax that was levied on non-Muslim citizens.
As a result, many Christians in Asia Minor converted en masse for purely economic reasons.