Decentralized and distributed model predictive control (DMPC) addresses the problem of controlling a multivariable dynamical process, composed by several interacting subsystems and subject to constraints, in a computation and communication efficient way. Compared to a centralized MPC setup, where a global optimal control problem must be solved on-line with respect to all actuator commands given the entire set of states, in DMPC the control problem is divided into a set of local MPCs of smaller size, that cooperate by communicating each other a certain information set, such as local state measurements, local decisions, optimal local predictions. Each controller is based on a partial (local) model of the overall dynamics, possibly neglecting existing dynamical interactions. The global performance objective is suitably mapped into a local objective for each of the local MPC problems.