A basic question in systems and control theory concerns the characterization of the set of all achievable closed-loop systems for a given plant system and a controller system to be designed. This problem is addressed in a general behavioral context. Sufficient, and often necessary, conditions for a behavior to be achievable are given, and for any achievable behavior a canonical controller is defined. The results generalize previously obtained results obtained for finite-dimensional linear systems. The application to nonlinear differential systems is outlined.