What is the relationship between revolution and terrorism? Much of the time, terrorism and revolution are taken to be distinct forms of political contention. This article argues that, to the contrary, their relationship is much closer than is often imagined. We show that a range of contemporary terrorist groups contain revolutionary elements: they seek to capture and hold territory, and see themselves as part of movements where the goal is to transform international as well as domestic orders. This provides two points of distinction: first, between ‘order-maintaining’ and ‘order-transforming’ goals; and second, between ‘minimalist’ and ‘maximalist’ tactics. The result is a taxonomy of different types of ‘revolutionary terrorism’. This analytic is used to dig deeper into the parameters of revolutionary terrorism, using militant Salafism as an example of a maximalist, order-transforming movement. A focus on transnational, order-transforming revolutionary terrorism generates a range of insights into the violent strategies, international dynamics and organizational forms used by Islamic State, al-Qaeda and related groups. The resulting research agenda, the article concludes, is rich in possibilities.