Vali Nasr's The Shia Revival: How conflicts within Islam will shape the future is a fast-paced and readable account of the history and current state of Shi'ite Islam. He covers the original schism between the followers of Ali (Muhammed's cousin) and the ruling Caliphs - a schism which may appear to be about religion now, but was essentially a power struggle. Most importantly, Nasr explains what the differences and animosities are now.
Shi'ites believe that the 12 Imams were able to extract an esoteric understanding of Islam that Sunnis don't believe exists. Sunnis insist that religious sources must be read literally and that the 12 Imams didn't have any deeper understanding than can be achieved by laymen.
Sunnis believe that worldly power, order and control embody a government with legitimacy, whereas Shi'ites believe legitimacy stems from being the best of Muslims (hence their support for Ali as the true Caliph and opposition to the Umyyad and Abbasid monarchies). Being in power and the Imams' failure to take power is taken by Sunnis as evidence against the right of the Imams to rule.
Sunnis don't believe that the Imam's have any better/deeper/esoteric or more insightful knowledge of Islam and don't believe in an intermediary between man and God. Sunnis also believe that the Shi'ite reverence for the Imams and other members of the Prophet Mohammed's family is heretical. For some Sunnis, even the Prophet Mohammed is not to be exhalted above any other Muslim. The Qu'ran is the only direct link to God.
Shia theologians reasoned that the [Twelth] imam's withdrawal must mean that in the interim before his return, political authority could never escape imperfection. Until the end of occultation, there could be no true Islamic rule, and anyone who claimed to be setting up such a regime would by definition be a pretender. Their goal from then on was to keep faith until the imam's return. Vali Nasr, The Shia Revival: How conflicts within Islam will shape the future
Henry Corbin characterised Shi'ism as Islam iraniene. My Iranian friend Kamran explained it to me thus: in order for Islam to consolidate itself as the state religion, it had become "Persianised" rather than the Persians becoming "Arabised". Appealing aspects of Zoroastrianism, rather than being left behind, were incorporated into Persian Islamic thought and practice. Islam colonised Persia and supplanted Zoroastrianism, but Zoroastrianism's revenge has been to fundamentally alter those parts of Islam is came into contact with.
The Islamic conquest of Persia and led to the demise of Zoroastrianism and the rise of Islam in Persia, but Shi'ism only really established itself in Persia when the Abbasid dynasty establish Shi'ite Islam as the state religion.
That is much like Christianity's encounters with animist local religions in Africa and South America, where attempts to completely displace the local gods and religious power-structure were not always successful. Either the missionaries themselves co-opted the local gods to their cause or they allowed the congregationists to take a lunch-buffet approach to their religion: snack on the interesting/meaty bits and leave the religious celery (bland, of no real use) for someone else. Or the Hare Krishna movement in the West (where Krishna has, for all intents and purposes, become nothing more than a blue Jesus).