  Containing the spreading of crime in urban societies remains a major
challenge. Empirical evidence suggests that, left unchecked, crimes may be
recurrent and proliferate. On the other hand, eradicating a culture of crime
may be difficult, especially under extreme social circumstances that impair the
creation of a shared sense of social responsibility. Although our understanding
of the mechanisms that drive the emergence and diffusion of crime is still
incomplete, recent research highlights applied mathematics and methods of
statistical physics as valuable theoretical resources that may help us better
understand criminal activity. We review different approaches aimed at modeling
and improving our understanding of crime, focusing on the nucleation of crime
hotspots using partial differential equations, self-exciting point process and
agent-based modeling, adversarial evolutionary games, and the network science
behind the formation of gangs and large-scale organized crime. We emphasize
that statistical physics of crime can relevantly inform the design of
successful crime prevention strategies, as well as improve the accuracy of
expectations about how different policing interventions should impact malicious
human activity deviating from social norms. We also outline possible directions
for future research, related to the effects of social and coevolving networks
and to the hierarchical growth of criminal structures due to self-organization.
