abstract: Population models have been used broadly to study the behaviour of systems formed by different kind of individuals. As a matter of fact, the theory of dynamical system is a fruitful field within Mathematics since a long time. A similar methodology can be used in Criminality to study the behaviour of societies whose individuals can be grouped according to their characteristics, for instance, economic income, culture, skills, profession, etc… In particular, we consider mathematical models of societies that are formed by (property) owners, criminals and guards, the three basic ingredients of the so called triangle dogma of criminality. After justifying these models, we present some analytical and numerical results. Finally, the useful of these models as well as their main drawbacks are discussed.