After Muhammad's death in 632 CE, the question of the leadership of the community will prove to be a serious challenge for Muhammad's followers. Nevertheless, within a few decades, the Arab armies will be in control of Iraq, Iran, Syria, Egypt, North Africa, Spain, Central Asia, and the Indian Subcontinent, and will establish a large empire.
Sources and Further Reading:
The History of al-Tabari
The Venture of Islam by Marshall G.S. Hodgson
The Early Islamic Conquests by Fred M. Donner