This paper reviews model predictive control (MPC) and its wide applications to both single and multiple autonomous ground vehicles (AGVs). On one hand, MPC is a well-established optimal control method, which uses the predicted future information to optimize the control actions while explicitly considering constraints. On the other hand, AGVs are able to make forecasts and adapt their decisions in uncertain environments. Therefore, because of the nature of MPC and the requirements of AGVs, it is intuitive to apply MPC algorithms to AGVs. AGVs are interesting not only for considering them alone, which requires centralized control approaches, but also as groups of AGVs that interact and communicate with each other and have their own controller onboard. This calls for distributed control solutions. First, a short introduction into the basic theoretical background of centralized and distributed MPC is given. Then, it comprehensively reviews MPC applications for both single and multiple AGVs. Finally, the paper highlights existing issues and future research directions, which will promote the development of MPC schemes with high performance in AGVs.