The output of a base chemical plant may take minutes or even hours to respond to the pressure of temperature changes imposed on the plant. In these cases, predictive control is required. Without a detailed running history of the chemical plant (in this example) it is then necessary to use model-based predictive control (rather than experience-based predictive control). This text is devoted to all aspects of model-based predictive control, including new developments in the theory of the subject and current applications of MBPC to real processes. Topics algorithm developments; industrial applications; and comparison with other approaches.