The end of the 2010s and the beginning of the 2020s have witnessed exponential progress in Artificial Intelligence (AI). As with other fields of human activity, the technology has started to percolate into extremism and terrorism. This chapter appraises the significance of extremist use of AI (or 'AI extremism'), proceeding in three steps. First, an introduction situates generative AI at the core of AI extremism and mentions illustrative cases. Second, two ideal-typical diagnoses-and therefore prognoses-of AI extremism are presented, which stand in opposition. On the one hand, an alarming diagnosis/prognosis casts AI as an overwhelmingly negative technological evolution bolstering online extremism and repression in critical and irreversible ways. On the other hand, a reassuring scenario stresses the technology's significant opportunities for counter-extremism and violence prevention, and highlights human societies' capacity to prevent nefarious dual-use through targeted policies, regulations, and interventions. However, an argument is made in a third step that both pessimistic and optimistic diagnoses/prognoses rest on the same simplistic narrative of an AI "revolution", interpreted either in a modern-liberal way emphasising progress or in a reactionary way emphasising regress, which is typical of reactions to important new technologies. Theories of historical state development indeed change the perspective through which we appraise AI, towards a third diagnosis/prognosis dialectically merging the two others, whereby AI simultaneously strengthens extremists and (strong) states, raising profound ethical questions.