In recent years, the global market for electric and hybrid vehicles has grown significantly, driving technological innovation in the automotive industry. Such growth has accelerated the development of vehicle dynamics control systems, which require efficient control strategies for optimal performance. This thesis investigates the use of the Koopman operator (KO) with model predictive control (MPC) for vehicle dynamics control. The Koopman operator provides a linear representation of nonlinear systems and enables simplified control of complex dynamical systems. By integrating KO with traditional nonlinear MPC, a Koopman MPC (KMPC) framework is developed that converts nonlinear to quadratic optimization problems, improving computational efficiency with minimal loss of accuracy. Three different methods for numerical KO identification are presented: extended dynamic mode decomposition (EDMD), deep dynamic mode decomposition (Deep-DMD), and a new method called enhanced EDMD (E²DMD). A KMPC-based torque vectoring algorithm is developed and compared with existing MPC strategies in a high-fidelity simulator. Furthermore, experimental validation using a scaled vehicle model demonstrates the potential of using Koopman-based controllers in real time on a standard embedded automotive platform. The thesis also presents a new method for generating Koopman operator learning data. The results point to promising future directions in the field of vehicle dynamics control.