This special issue is one of the very first dedicated to crime modelling in a journal of applied mathematics. It emphasizes one of the new areas at the Social Science frontier, where modelling and mathematical tools are put to use with a view to shed light on phenomena previously thought to be outside of their reach. Pioneering research is increasingly being carried out in many different areas in the life sciences or social sciences, often under the heading of the study of complex systems. When addressing issues regarding society, individuals or the collective behaviours of humans, several questions naturally arise about the modelling enterprise. What is the nature and role of modelling in social sciences? What is one to expect from these new approaches? The case of economics, which has relied on mathematics for a very long time now, can serve as a paradigm for what is happening in other social sciences.