In the middle east Islam's spread was twofold. Firstly through the Muslim conquest which established the ruling class as Muslim and Arabic in culture. In former Byzantine possessions where sectarianism was rife, the fact that Muslims didn't discern against different denominations meant that the mainly Christian population of Egypt and the Levant was happier under Muslim rule than Byzantine. The second wave is the conversion of the population, which happened at a very slow rate. Christianity was still the major religion in Mediterranean Muslim regions centuries after the first conquest. There were financial benefits to converting, nonbelievers had to pay a higher tax than Muslims. Additionally Islam was the religion of the ruling and military classes, those with aspirations in those spheres would have to change their beliefs.

Further afield is a similar two fold story, only the introduction of Islam is through the mercantile classes which operated the Indian ocean or transaharan trade routes. Eventually the ruling classes again became Muslim, in Africa through conversion and in India through a series of invasions from the west and central Asia. Once again, the general population slowly followed suit.

Colonialism didn't really reach Asia until the late 1700s and Africa until the mid 1800s. European presence in these areas were usually limited strictly to coastal areas beforehand and with too little personnel to make a difference. The middle east remained under Ottoman rule until 1918 and Iran stayed independent. In India the British did attempt to evangelise but were forced to be tolerant to the well established religions of Hinduism and Islam, which were already intertwined with the caste system. Resultantly, the mercantile classes and maharajas remained their old religions, so the most conversions in India came from the lowest caste, those with the least influence.