Criminology is intrinsically a pluri-disciplinary subject. Along history different schools of thought have proposed different and sometimes conflictive ways of considering crime. We are interested in the possible contributions of mathematical modeling. In an attempt to discover stylized trends worth of being understood through simple models, we referred to numerous and quite recent papers that analyze and discuss empirical data. In the following we summarize part of this literature trying to extract general conclusions. Then we present some recent modeling attempts that may help to understand the large variance in the statistical based conclusions.