This chapter reviews some recent results on the boundary stabilization of different classes of partial differential equations. In order to provide a self-content chapter with consistent control objectives and notation, we first review the finite-dimensional case. Controllability and observability conditions for linear ordinary differential equations are recalled together with some basic Lyapunov theory for the stability analysis and the design of saturated controllers. Then we address the boundary control problem for the stabilization of a reaction-diffusion equation by means of numerically tractable design methods while considering different norms and possible constraints on the amplitude of the inputs. Finally similar control design problems will be studied for the stabilization of the Korteweg–de-Vries equation and the wave equation.