This paper addresses three aspects of receding horizon control in discrete-time : (1) feedback stabilization of general nonlinear systems with receding horizon control; (2) the generation of stabilizing feedback control laws that are discontinuous in the state; and (3) the suitability of receding horizon control to stabilize feedback-linearizable systems. The nonlinear receding horizon controller is shown via a Lyapunov function argument to be asymptotically stabilizing for a large class of nonlinear systems. As a special case, nonlinear systems that can be locally feedback linearized can be locally asymptotically stabilized with nonlinear receding horizon control. A simple example shows that there exist controllable nonlinear discrete-time systems that cannot be asymptotically stabilized with continuous feedback. For this example, the nonlinear receding horizon controller generates an asymptotically stabilizing feedback law. The discontinuity in the resulting feedback law is discussed and numerical results are provided.