In this thesis we present mathematical models that describe social phenomena such as economic dynamics, criminology and tax evasion. In the first chapter we describe the evolution of the distribution of wealth in society. Firstly, we use compartmental model where we divide the society into the n classes depending on their social index, and later we introduce the generalization of the model with continuous model where the dynamics of society are influenced by economic mobility, i.e. the change in the social index. Then, in the second chapter, we aim at further understanding the theoretical mechanisms in criminology. We have an approach that helps us to better understand the facts that characterize modeling in criminology and plan crime prevention strategies. We introduce a class of models based on Lotka-Volterra’s theory of ”predator-prey” populations where we present a triangle model consisting of sub-populations of criminals, guards and targets, and a model of drug production and sales where we have sub-populations of dealers and drug manufacturers. Next, we present the class of epidemiological models where recruitment among sub-populations occurs with some type of ”infection”. Here we describe a model of poverty and crime, and a model of four sub-populations where we have sub-populations of criminals, those who are not susceptible to commit a crime, those who are susceptible to commit a crime and prisoners. Finally, we introduce a more complex approach to the problem that takes into account the socio-economic dynamics introduced in the first chapter. In the last chapter, we describe models based on cellular automata where we consider a particular kind of crime, i.e. tax evasion. Using a two-dimensional cellular automata approach, we present a model where an individual can either be contributor (tax payer) or no contributor (tax evader or cheater). At the end of the chapter we expand the model by introducing the fiscal policy.