Cyber-physical systems have developed into a very active research field, with a broad range of challenges and research directions going from requirements, to implementation and simulation, as well as validation and verification to guarantee essential properties. In this survey paper, we focus exclusively on the following fundamental issue: how to link physicality and computation, continuous time-space dynamics with discrete untimed ones? We consider that cyber-physical system design flow involves the following three main steps: 1) cyber-physical systems modeling; 2) discretization for executability; and 3) simulation and implementation. We review—and strive to provide insight into possible approaches for addressing—the key issues, for each of these three steps.