A caliphate (from the Arabic خلافة or khilāfa, Turkish: Hilafet) is a Muslim spiritual community led by a supreme religious (and even political) leader known as a caliph (meaning literally a successor, i.e. a successor to the prophet Mohammad). The term caliphate is often applied to successions of Muslim empires that have existed in the Middle East and Southwest Asia. Conceptually the caliphate represents the political unity of the entire community of Muslim faithful (the ummah) ruled by a single caliph. In theory, the organization of a caliphate should be a constitutional republic (the Constitution being the Constitution of Medina), which means that the head of state, the Caliph, and other officials are representatives of the people and of Islam and must govern according to constitutional and religious law, or Sharia. In its early days, the first caliphate resembled elements of direct democracy (see shura) and an elective monarchy.
It was initially led by Muhammad's disciples as a continuation of the leaders and religious system the prophet established, known as the 'Rashidun caliphates'. A "caliphate" is also a state which implements such a governmental system.
Sunni Islam stipulates that the head of state, the caliph, should be elected by Shura – elected by Muslims or their representatives. Followers of Shia Islam believe the caliph should be an imam chosen by God from the Ahl al-Bayt (Muhammad's purified progeny). From the end of the Rashidun period until 1924, caliphates, sometimes two at a single time, real and illusory, were ruled by dynasties. The first dynasty was the Umayyad. This was followed by the Abbasid, the Fatimid (not recognized by Muslims outside the Fatimid domain), and finally the Ottoman Dynasty.
The caliphate was "the core leader concept of Sunni Islam, by the consensus of the Muslim majority in the early centuries."
Read more about Caliphate: History, Re-establishment of The Caliphate, Famous Caliphs