In this chapter we present some of the central philosophical issues emerging from the increasingly expansive and sophisticated roles computational modeling is playing in the natural and social sciences. Many of these issues concern the adequacy of more traditional philosophical descriptions of scientific practice and accounts of justification for handling computational science, particularly the role of theory in the generation and justification of physical models. However, certain novel issues are also becoming increasingly prominent as a result of the spread of computational approaches, such as nontheory-driven simulations , computational methods of inference, and the important, but often ignored, role of cognitive processes in computational model building.Most of the philosophical literature on models and simulations focuses on computational simulation, and this is the focus of our review. However, we wish to note that the chief distinguishing characteristic between a model and a simulation (model) is that the latter is dynamic. They can be run either as constructed or under a range of experimental conditions. Thus, the broad class of simulation models should be understood as comprising dynamic physical models and mental models, topics considered elsewhere in this volume.This chapter is organized as follows. First in Sect. 5.1 we discuss simulation in the context of well-developed theory (usually physics-based simulations). Then in Sect. 5.2 we discuss simulation in contexts where there are no over-arching theories of the phenomena, notably agent-based simulations and those in systems biology. We then turn to issues of whether and how simulation modeling introduces novel concerns for the philosophy of science in Sect. 5.3. Finally, we conclude in Sect. 5.4 by addressing the question of the relation between human cognition and computational simulation, including the relationship between the latter and thought experimenting.