After briefly overviewing the application problems that call for boundary control method and the existing techniques for control of PDEs, the paper introduces the key concepts for spatially continuous backstepping control design for PDE systems. After that, a general procedure for parabolic PDEs of a "spatially causal" class is presented, followed by a discussion of the main design equations for gain computations. For PDE systems with boundary sensors a backstepping observer design is introduced. The paper concludes with the application of the backstepping method to the Schrodinger equation and first-order hyperbolic PDEs (the transport equation and its derivatives).