Social choice theory provides a theoretical framework for analyzing how to combine individual opinions, preferences, interests or welfare so as to reach a collective decision. Social choice theory is one of the areas in economics that has seen a boom in simulations work using models based on the behavior of individuals involved in collective decision-making. The purpose of this paper is to oer to the uninitiated reader a methodological presentation of these dierent models, as well as the techniques for theoretical calculations and simulations, and then to report on recent developments concerning new models and advances in calculation techniques and simulations. This paper will thus give readers easy access to the models which, due to their complexity, might seem to be reserved for initiates. We take the opportunity to present and discuss the assumptions that support each of the models, and indicate how simulations may be helpful in analyzing complex problems in social choice theory.