After Ali's death, Shi'as believed his son, Hasan, should be the next leader but there was a disagreement.
Ali had been opposed by Muawiya (Uthman's cousin)+ Hasan agreed that his family would lead the caliphate only after Muawiya had died.
Unfortunately, Hassan died and Muawiya made his son, Yazid, the leader. Hasan's brother, Husayn, refused to accept Yazid and war broke out.