The paper of Enrique Zuazua is organized as follows. Section 2 describes the main issues related to the controllability of the linear wave equations. In Section 3 the author discusses the controllability of wave equations under certain conditions. Section 4 contains the detailed discussion regarding the controllability of the heat equation. Section 5 presents a fixed point method which allows to prove the approximate controllability of the semilinear heat equation with globally Lipschitz nonlinearity. This is followed by the analysis of the controllability of the Galerkin approximations of the Navier-Stokes equations in Section 6 and by some open problems related to the mentioned topics.