Ali, the cousin and son-in-law of the prophet was the fourth caliph and, according to the Shi'ites, the first to rightly succeed him. Ali was assassinated by rivals in Iraq and later, his son, Hussein was also killed at Kerbala. This led to a revolt against the Ummayid caliphate, an event celebrated in the festival on the 10th of the month of Muhurram. Shi'ites believe in a kind of apostolic succession of Imam (supreme and infallible leader).
However, the 12th Imam disappeared in around 873CE since when a line of caretaker leaders or Ayatollah have kept the faith guarded. Shia Muslims believe that the 'hidden Imam', a kind of messianic figure, will return someday and provide salvation for the faithful. Overall, Shi'a Islam is more esoteric and emotional than its Sunni counterpart.