How did Islam spread throughout the world?

According to the most authoritative historical narratives, the process was mixed.

Islam spread throughout Arabia and entered the Horn of Africa during the early period as Muslim refugees fled the persecution. Eventually, the Muslims in Arabia developed a state and through da'wa and invitation to other nations, preaching, trade, intermarriage and military expansion Islam spread.

Instances of Muslim military expansion are often not well understood. For example, it is not common knowledge that the intervention of Muslims was sought by oppressed groups in both Spain and Persia during the 7th century. Meanwhile, North Africa and Egypt were part of the Byzantine Empire until the Byzantines conducted aggressive military maneuvers near the Arabian border. When the Muslims responded in kind, war ensued and the Byzantine Empire lost much of its territory to the Muslims.

When the new Muslims conquered Egypt, Persia, North Africa and India they became the rulers in those areas. However, in these same places, it often took centuries for populations to convert to Islam, mainly through interaction, intermarriage and missionary efforts that emphasized spirituality (Sufism). Some rulers in the early years of Islamic rule (the Umayyads) actually discouraged conversion, most likely because adult men who converted would no longer pay jizya and would be eligible to join the military. Jizya was a tax paid to the government by non-Muslim men in lieu of their military service (however they were then not required to pay Zakat, which was required of Muslims to aid the poor). Moreover, significant groups living under Muslim rule, such as Christians in Lebanon and Hindus in India, never converted and continued to practice their religions until the present. In other areas, Islam spread mainly through trade and Sufi missionary activity.