Mathematical models are finding an increasing use in bio-medical scientific investigations as effective means of putting the interpretation of biological phenomena on a more quantitative basis. Besides the well established mathematical paradigm based on differential equations, another approach that takes full advantage of the steadily increasing computing power, is gaining increasing consensus: micro-simulation. Micro-simulation is based on the idea of mimicking the behavior of the system under investigation through the specification of the rules of interaction among its individual constituents. This rule-driven (sometimes called equation-free) approach allows a smoother upgrade of models sophistication and reduces the gap between the abstract level of description typical of mathematical models and the complexity of the biological world. In this article we aim at illustrating, through specific examples, some of the potential advantages that micro-simulation has to offer in order to gain a better grasp and understanding of complex phenomena in biology and medicine.