The recent years have seen spectacular advances in our understanding of the structure of complex networks, providing detailed maps of social and technological systems, cellular networks and food webs. The ultimate goal of these efforts is to be able to translate these topological findings into dynamical predictions on the system's observable behavior. However, our progress in this direction is hindered by a crucial lacuna: the absence of microscopic models that describe the dynamics of many of the relevant complex systems. The challenge is that these systems are, in effect, a black box. We can observe their macroscopic behavior, e.g., track the spread of an epidemic, but we have no direct access to the microscopic exchanges taking place between the nodes, i.e. the dynamical model that most accurately describes the processes of infection and recovery. Metaphorically, the task of unveiling these microscopic dynamics, is equivalent with an attempt to recover the structure of a car's engine directly from observations of its macro-scale behavior, having no direct access to what is under the hood. Hence we developed a reverse engineering method to infer the microscopic dynamics of a complex system directly from observations of its response to external perturbations. The formalism allows us to construct the most general class of continuum models that are consistent with the observed behavior.