I don't know if this has been done here before. But it strikes me that the rise (and fall) of ISIS' caliphate poses a few questions that could make for interesting alternative history. Before we get started, it should not need explaining that I condemn ISIS. The point of this thread is more the theoretical significance of the idea, of creating a "caliphate" in eastern Syria and western Iraq, which has historical and religious implications.
Theoretically, the caliph is the successor to the prophet Muhammad. The role combines enormous religious authority with secular power. In theory, all Muslims would be obliged to follow the caliph's guidance. This includes the obligation to jihad, which typically refers to a spiritual struggle to master one's emotions and become a better person, but can also mean armed struggle if necessary in defence of the ummah.
The basis of the caliphate would be predominantly Sunni Arab areas in western Iraq and eastern Syria. The demography here "fits" a new state better than the Shia led governments in Baghdad and Damascus.
Returning to the caliph, there has been no caliph since the last holder of that title was abolished in 1922 in Turkey. That is significant for several reasons. First, it means that in theory there can be no Sharia without a caliph, and therefore no ultimate guarantee of a just society. Second, historically the office of caliph was debased over time, as at one point there were 3 different empires claiming the title. But a "revival" of the concept would be a singular claimant to the title.
Obviously, there are significant problems. In reality, the actual ISIS caliphate was universally rejected by all the major authorities of the Islamic world and condemned by everyone from Egypt's grand Mufti to the governments of every Muslim country, many of whom participated in the bombing of ISIS targets, including planes from Morocco, Jordan and several other countries. Plus it goes without saying that the Shia everywhere were opposed to the new state.
Perhaps the biggest failing of ISIS though was its brutality. They achieved the incredibly rare feat of uniting practically the entire world against them. Their evil acts horrified and shocked the world, provoking their own destruction.
Suppose the new "caliphate" had taken a completely different approach, though. Let's say one that (initially at least) confined itself to local goals only. Could such an entity have successfully established itself? And what effect would this have on the world, if it had?