With the death of Ali, the Sunni/Shi’i schism started. He was murdered. There are no ‘Rashidun’ (rightly guided Caliphs) after him. A war followed his death during which the Umayyads took over (Syria).
The Shi’i further divided into 7ers and 12ers, depending on which branch you followed. The Caliphate broke apart after the Abbasids came from Persia/Iran, and ruled until Genghis Khan destroyed them, ending with the burning of the library at Alexandria.
Commemorating Aashura is really important to Iran/all of the Shi’a.
Have studied the culture since the early 1960s myself.