Short answers, pulled from the story.
The schism began in 632 CE following the death of Prophet Muhammad. This event ignited a division that defined the next fourteen centuries of Islamic history.
The Battle of Karbala in 680 CE cemented the Shia identity as a distinct sect. During this battle, Husayn ibn Ali and his followers were massacred by the Umayyad army, establishing a narrative of righteous suffering against tyranny.
The Twelver branch follows a line of twelve Imams beginning with Ali and ending with Muhammad al-Mahdi. Muhammad al-Mahdi is believed to be in a state of occultation until he returns to establish justice before the Day of Judgment.
Shah Ismail I of the Safavid Empire declared Twelver Shia Islam the official state religion of Persia in 1501. This decision shifted the religion from a predominantly Arab phenomenon to a predominantly Persian one.
The Zaydi branch is found primarily in Yemen and differs significantly by rejecting the doctrine of infallibility. Zaydis believe that any descendant of Ali and Fatima who rises in rebellion against a corrupt ruler can become the Imam.
The holiest sites for Shia Muslims are the shrines of Ali in Najaf and Husayn in Karbala. Additional mausoleums of various Imams are located in Mashhad and Qom.