First are the Rashidun caliphs of Medina, beginning with Muhammad's father-in-law Abu Bakr and ending with Muhammad's son-in-law Ali (and briefly Ali's son Hassan). Next are the Umayyad caliphs of Damascus, who were relatives of the third Rashidun caliph Uthman. In 750 the Umayyads were overthrown by the Abbasids who were descendents of Muhammad's uncle Abbas and who ruled from Baghdad. Over centuries the Abbasids lost territory and power, and in 1258 the Mongols sacked Baghdad and executed the caliph there. After this, the ruling Mamluks of Egypt installed a line of the Abbasid family as caliphs in Cairo, but they held only ceremonial powers. When the Mamluks were defeated by the Ottoman Empire, the Ottoman sultans (beginning with Selim I) assumed the title. The office was abolished 1924, shortly after the formation of the modern country of Turkey.
Others have held the title of caliph, including the Umayyads of Córdoba and the Fatimids of North Africa, but they are not included on these lists.