Hazrat Ali had two descendants, Hazrat Imam Hussain and Hazrat Imam Hassan. Hussain was the ruler of the part of the empire known today as Iran. The other part in modern Iraq was ruled by the Umayyads.
Hussain was called upon by the Shiahs of Kufa, a small town in the Umayyad kingdom, to accept their allegiance and claim his place as the leader of the Islamic community.
This was against the wishes of the ruler of Kufa, Yazid, who instructed his governor, Ibn-e-Ziad to take appropriate action.