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What does Ashura celebrate?
Actually, it’s not a celebration. The day marks the martyrdom of Imam Hussein, the son of Ali. Ali was Muhammad’s cousin, son-in-law and, after Muhammad’s death, his caliph. But Shia Muslims believe Muhammad designated Ali as his rightful immediate successor, while Sunnis accept him as the fourth caliph, after several of Muhammad’s companions.
That’s the root of the major sectarian split in Islam: Sunnis believe the community should just pick the best man for the job, while Shias believe leadership of the Muslim world should pass through the Prophet Muhammad’s bloodline.
After Ali was killed, Shias believe that his son Hussein was the rightful leader of the Muslim community because of his matrilineal descent from Muhammad. In 680 A.D., Hussein and his supporters refused to submit to the oppressive rule of the Umayyad caliph, Yazid. As Hussein and his family attempted to leave Mecca, Yazid’s forces clashed with Hussein's caravan at Karbala, in present-day Iraq. The bloody battle at Karbala ended with Hussein martyred and then beheaded.
That scene – the suffering and sacrifice of the figure Shias see as Muhammad’s true heir – has been formative to Shia identity and theology.