The prototypical problem in control theory is the stabilization of a set point. When, instead of a set point, a time-varying reference needs to be stabilized, then the problem is called trajectory tracking. Typical examples of trajectory-tracking problems are set point changes along precomputed references, synchronization tasks or startup of processes. While stabilization and trajectory tracking are well-understood for a wide range of systems, not all control tasks arising in practice belong to these categories. In robotics, for example, it is frequently required to move a robot along a geometric curve without any preassigned timing information. In other words, the speed to move along the curve is a degree of freedom. Such problems are called path-following problems. This book deals with nonlinear model predictive control (NMPC) for constrained trajectory-tracking and path-following problems. Based on a detailed problem analysis a framework to tackle these problems is developed. Examples from robotics and chemical engineering are used to illustrate the results. The main concerns of this book are twofold: On the one hand, it is shown that nonlinear model predictive control is very well applicable to problems beyond set point stabilization. On the other hand, it is demonstrated that path-following concepts provide a suitable framework for many challenging control problems ranging from robotics to chemical engineering.