One significant issue is that Sunnis believed that only the most pious of the Prophet's disciples should become caliphs, but the Shiites argued that succession should be based on bloodline. Abu Bakr succeeded Muhammad, but Shiites wanted Ali, a cousin of the Prophet, to become caliph.
Abu Bakr was Muhammad's father-in-law, and Ali was the Prophet's son-in-law. Shiites do not acknowledge the first three caliphs, and they believe that Ali is the most divine man after the Prophet. However, the Sunnis believe that Ali was one of the rightful heirs of Muhammad. Shiites also believe that imams should reign as leaders in the Islamic world. Sunni doctrine typically falls under the guidance of the state, but Shiites maintain that imams are the ultimate authority and not the state.