Control theory aims to find a control that will lead the given state of the system (often described by a partial differential equation (PDE)) in a desirable situation. On the other hand, homogenization theory is concerned with the analysis of the effects of high-frequency oscillations in the coefficients or in the domain, upon the solutions of a PDE. In this talk, I will present the interplay of these two concepts in the context of the approximate controls for some classes of PDEs with periodic rapidly oscillating coefficients. In the first case, we consider a parabolic problem in composites with a periodic interfacial resistance. In another, we study a semilinear elliptic equation in perforated domains. In both cases, we first prove the approximate controllability of the problem as well as the homogenized ones. Then we show that the control and the corresponding solution of the periodic problem converge respectively to the control and to the solution of the homogenized problem.