Distributed Model Predictive Control (DMPC) is a control strategy for large-scale systems where multiple local controllers manage subsets of inputs and outputs. It is particularly useful when a centralized controller is not feasible due to computational or organizational constraints. DMPC can be decentralized, noncooperative, or cooperative. Cooperative DMPC, where all local controllers optimize a common objective, offers stronger theoretical guarantees and better performance. The paper discusses the formulation of DMPC for constrained linear systems, where each subsystem has its own state, input, and output. The dynamics of each subsystem are influenced by neighboring subsystems, and the overall system is optimized through a cooperative approach. The cooperative DMPC algorithm involves solving a finite-horizon optimal control problem (FHOCP) for each subsystem, with the solution being a convex combination of the previous iteration and the newly computed solution. This ensures convergence to the centralized optimum and guarantees closed-loop stability. The algorithm is designed to handle input and state constraints, and it can be extended to include output feedback and offset-free tracking. For nonlinear systems, cooperative DMPC has been proposed, where each local controller considers the dynamics of its subsystem and interactions with neighbors. Non-convexity of the optimization problem can be addressed by removing the least effective control sequences. The paper also discusses future directions in DMPC research, including nonlinear DMPC, economic DMPC, reconfigurability, constrained distributed estimation, and specific distributed optimization algorithms tailored for DMPC problems. These advancements aim to improve the effectiveness and robustness of DMPC in various applications.Distributed Model Predictive Control (DMPC) is a control strategy for large-scale systems where multiple local controllers manage subsets of inputs and outputs. It is particularly useful when a centralized controller is not feasible due to computational or organizational constraints. DMPC can be decentralized, noncooperative, or cooperative. Cooperative DMPC, where all local controllers optimize a common objective, offers stronger theoretical guarantees and better performance. The paper discusses the formulation of DMPC for constrained linear systems, where each subsystem has its own state, input, and output. The dynamics of each subsystem are influenced by neighboring subsystems, and the overall system is optimized through a cooperative approach. The cooperative DMPC algorithm involves solving a finite-horizon optimal control problem (FHOCP) for each subsystem, with the solution being a convex combination of the previous iteration and the newly computed solution. This ensures convergence to the centralized optimum and guarantees closed-loop stability. The algorithm is designed to handle input and state constraints, and it can be extended to include output feedback and offset-free tracking. For nonlinear systems, cooperative DMPC has been proposed, where each local controller considers the dynamics of its subsystem and interactions with neighbors. Non-convexity of the optimization problem can be addressed by removing the least effective control sequences. The paper also discusses future directions in DMPC research, including nonlinear DMPC, economic DMPC, reconfigurability, constrained distributed estimation, and specific distributed optimization algorithms tailored for DMPC problems. These advancements aim to improve the effectiveness and robustness of DMPC in various applications.