Complex systems offer broad, unique research challenges due to their inability to be understood through a classic reductionist perspective, as they exhibit emergent phenomena that arise through the interactions of their components. In this thesis, we briefly review some characteristics of complex systems and the interplay of mathematical and computational methods to study them. We then discuss these approaches, how they are implemented, and how they support one another in three settings. First, we present a study that connects weather data to seasonal population-abundance of mosquitoes, using a microscopic model. Secondly, we consider the collective motions that arise in ensembles of disks interacting through non-elastic collisions and investigate how such behaviors affect macroscopic transport properties. Finally, we consider a 'self-sorting' one-dimensional collection of point-particles. In all of these cases, agent-based models and simulations are used to guide analysis, and in the final example, we explain how the simulations led to new theorems. Articles and molecular dynamics computer codes are provided as appendices.