Recent years have witnessed an increased interest in model predictive control (MPC) for fast applications. At the same time, requirements on engines and vehicles in terms of emissions, consumption and safety have experienced a similar increase. MPC seems a suitable method to exploit the potentials of modern concepts and to fulfill the automotive requirements since most of them can be stated in the form of a constrained multi input multi output optimal control problem and MPC provides an approximate solution of this class of problems. In this introductory chapter, we analyze the rationale, the chances and the challenges of this approach. This chapter does not intend to review all the literature, but to give a flavor of the challenges and chances offered by this approach.