Muhammad died in 632 without, on the Sunni account, naming a successor. A gathering of Medinan and Meccan leaders at the portico of the Banu Saida acclaimed Abu Bakr, his close companion and father-in-law, as khalifa, deputy or successor. Ali, the Prophet's cousin and son-in-law, was occupied with the burial and was not present; Sunni tradition holds that he accepted the outcome, Shia tradition that he was presented with a fait accompli.
Abu Bakr's two years were spent holding the Arabian coalition together by force. Umar, who followed for a decade, presided over the conquest of Syria, Egypt and Sasanian Iraq, established the Muslim calendar and much of the administrative apparatus, and was assassinated by a Persian captive in 644. Uthman, of the Umayyad clan, oversaw the compilation of a standard text of the Quran and the destruction of variant copies, an act of lasting consequence, and was killed by mutineers in 656 amid accusations of nepotism. Ali was acclaimed in the ensuing crisis, fought Aisha and her allies at the Battle of the Camel and Muawiya at Siffin, saw a faction secede from his own camp over his agreement to arbitration, and was assassinated by one of those seceders in 661.
Sunni tradition calls these four al-Rashidun, the rightly guided, and treats the period as the closest approximation of government under prophetic norms. It does not treat it as peaceful. Three of the four were murdered, the community fought a civil war, and the Sunni sources record all of it. The claim is about the legitimacy of their authority and the quality of their intention, not about the tranquillity of their reigns.