ISIS wants to establish a caliphate

Since pledging allegiance to al-Qaeda in 2004, the group's goal has been remarkably consistent: found a hardline Sunni Islamic state. As General Ray Odierno puts it: "They want complete failure of the government in Iraq. They want to establish a caliphate in Iraq." Even after ISIS split with al-Qaeda in February 2014 (in large part because ISIS was too brutal even for al-Qaeda), ISIS' goal remained the same.
Today, ISIS holds a fair amount of territory in both Iraq and Syria — a mass roughly the size of Belgium. One ISIS map, from 2006, shows its ambitions stopping there — though interestingly overlapping a lot of oil fields:

ISIS/Aaron Zelin

Another shows their ambitions stretching across the Middle East, and some have apparently even included territory in North Africa:

Ali Soufan/ISIS

Now, they have no chance of accomplishing any of these things in the foreseeable future. ISIS isn't even strong enough to topple the Iraqi or Syrian governments at present. But these maps do tell us something important about ISIS: they're incredibly ambitious, they think ahead, and they're quite serious about their expansionist Islamist ideology.