"Successor" to the Prophet Muhammad's political and religious leadership of the Muslim community (but not to his prophetic role.)
The first four caliphs, Abu Bakr, `Umar, `Uthman, and `Ali, are called the "Rightly Guided Caliphs." The Caliphate subsequently was handed down in dynastic succession by the Umayyads and the Abbasids; thereafter many rulers claimed the title of Caliph, including most notably the Ottomans.