This monograph presents a unified synthesis on how to design robust and predictive control approaches for discrete-time Linear Parameter Varying (LPV) systems. In particular, some recent results concerning LPV state-feedback design using the H∞ framework and Model Predictive Control for LPV systems are presented. Thereafter, both approaches are illustrated in several important case studies for automotive applications. Firstly, the lateral steering control of autonomous vehicles is considered. Then, an application to Advanced Driver Assistance Systems is presented, where MPC and LPV approaches are integrated in view of optimal selection of the scheduling parameter. This monograph will be of interest to students, researchers and professionals who want to learn more about designing robust and predictive control approaches for discrete-time Linear Parameter Varying systems.