  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.
