<p>Model Predictive Control (MPC) has become a revolutionary control method in current engineering practice, offering explicit benefits over previous approaches. It explicitly considers models of the system, constraints, and interactions among multivariable systems as an integral part of the decision-making process. The review’s subject provides context on the theoretical underpinning of MPC, its subsequent methodology development, and meta-areas of application since its inception as a control paradigm in the 1970s, up to today, where it is viewed as a flexible and sophisticated control paradigm. The Nonlinear, Robust, Stochastic, Adaptive, and Explicit variants of MPC are discussed here in terms of their optimisation models, computing requirements, and uncertainty computational needs. Specific consideration is given to computational issues, such as model accuracy and real-time optimisation, as well as newer methods, including sequential quadratic programming, real-time iteration schemes, model reduction, and integrating machine learning. In addition, the concepts of Distributed MPC and Economic MPC are introduced as the new paradigm dealing with the achievement of scalability goals and performance economy when working in large-scale and cost-effective systems. MPC flexibility and cost potential are shown through case studies in process industries, energy systems, aerospace, robotics, and manufacturing. With its advantages, much of the computational intensity, modelling, and implementation complexity is an active research frontier. In the future, connecting to machine learning, high-performance computing, and distributed control architectures will likely increase the importance and potential of MPC. In general, MPC remains a foundation of control engineering, and provides powerful, flexible, and cost-effective solutions to what have become more challenging systems.</p>