Replication in the behavioral sciences is a matter of considerable debate. We describe a series of fundamental interrelated conceptual and methodological issues with current research that undermine replication and we explain how they could be addressed. Conceptually, we need a shift (1) from verbally described theories to mathematically specified theories, (2) from lineal stimulus-cognition-response theories to closed-loop theories that model behavior as feeding back to sensory input via the environment, and (3) from theories that ‘chunk’ responses to theories that acknowledge the continuous, dynamic nature of behavior. A closely related shift in methodology would involve studies that attempt to model each individual’s performance as a continuous and dynamic activity within a closed-loop process. We explain how this shift can be made within a single framework – perceptual control theory - that regards behavior as the control of perceptual input. We report evidence of multiple replication using this approach within visual tracking, and go on to demonstrate in practical research terms how the same overarching principle can guide research across diverse domains of psychology and the behavioral sciences, promoting their coherent integration. We describe ways to address current challenges to this approach and provide recommendations for how researchers can manage the transition.