The rapid spread of radical ideologies has led to a world-wide succession of terrorist attacks in recent years. Understanding how extremist tendencies germinate, develop, and drive individuals to action is important from a cultural standpoint, but also to help formulate response and prevention strategies. Demographic studies, interviews with radicalized subjects, analysis of terrorist databases, reveal that the path to radicalization occurs along progressive steps, where age, social context and peer-to-peer exchanges play major roles. To execute terrorist attacks, radicals must efficiently communicate with one another while maintaining secrecy; they are also subject to pressure from counter-terrorism agencies, public opinion and the need for material resources. Similarly, government entities must gauge which intervention methods are most effective. While a complete understanding of the processes that lead to extremism and violence, and of which deterrents are optimal, is still lacking, mathematical modelers have contributed to the discourse by using tools from statistical mechanics and applied mathematics to describe existing and novel paradigms, and to propose novel counter-terrorism strategies. We review some of their approaches in this work, including compartment models for populations of increasingly extreme views, continuous time models for age-structured radical populations, radicalization as social contagion processes on lattices and social networks, agent based models, game theoretic formulations. We highlight the useful insights offered by analyzing radicalization and terrorism through quantitative frameworks. Finally, we discuss the role of institutional intervention and the stages at which de-radicalization strategies might be most effective.
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