In the period following the death of The Prophet, there was a large power gap in the leadership of Islam. In 661 C.E., about thirty years after Muhammad's death, eventually a line of caliphs or, literally "successors", who claimed descent from The Prophet's uncle Umayya, secured the spiritual and temporal leadership of Islam. This was the source of the major schism in Islam, between the sunni and shi'i: the shi'i maintained that legitimate leaders of the Muslim world, who they termed Imams, could only be lineally descended Muhammad's cousin Ali, while the sunni, who formed the large majority, maintained that anybody who was of The Prophet's bloodline and was acclaimed by the majority of Muslims could serve.
The Umayyad Caliphs enjoyed wide popular support at first, and expanded the military conquests the Arabs had made at the time of the Islamic Revolution. However, support for them waned over time. This was the result of misrule on the part of the Umayyads, and, after pushing as far north as France, military setbacks and discontent in the ranks of the soldiers, and smoldering discontent on the part of the substantial shi'i minority. The Umayyads themselves proved to be their own worst enemies, behaving more like kings than religious leaders - rumors were rampant of the caliphs drinking wine and having promiscuous sex, hardly appropriate for the leaders of a religion that forbids both.
This discontent expressed itself in a series of regional revolts and shi'i uprisings, and by 747 C.E., a general uprising in the Muslim world. The revolt swept the Umayyads out of power very quickly, and 750 C.E., their dynasty had lost power everywhere except in Moorish Spain, where they would hold onto power for several hundred more years. They were replaced everywhere else by the Abbasid Caliphs, who claimed descent from The Prophet's other uncle, Abbas.