Abstract Linear model predictive control (LMPC) is well established as the industry standard for controlling constrained multivariable processes. A major limitation of LMPC is that plant behavior is described by linear dynamic models. As a result, LMPC is inadequate for highly nonlinear processes and moderately nonlinear processes which have large operating regimes. This shortcoming coupled with increasingly stringent demands on throughput and product quality has spurred the development of nonlinear model predictive control (NMPC). NMPC is conceptually similar to its linear counterpart except that nonlinear dynamic models are used for process prediction and optimization. The purpose of this paper is to provide an overview of current NMPC technology and applications, as well as to propose topics for future research and development. The review demonstrates that NMPC is well suited for controlling multivariable nonlinear processes with constraints, but several theoretical and practical issues must be resolved before widespread industrial acceptance is achieved.