What accounts for the continued spread of islam in the early modern era and for the emergence of reform or renewal movements within the islamic world?

We can name three big reasons here.
1. The conversion to Islam in the early age was not something sudden and it did not mean that the previous religious convictions of the population were abandoned. The way it worked was that the Islamic practices were integrated into existing religious systems.
2. Second one is the traveling religious men who went and spread the faith. Wondering holly men were peaceful and were not perceived as threats.They were educated and often were healers. This allowed them to intermingle in the other societies and be their connection to the Islamic world.
3.The renewal movements or the reform ones were created in response to this intermingling of Islam with other religious doctrines. They wanted to return to the true faith and keep Islam pure. They wanted to purify it from foreign influences.