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This paper introduces some recent developments on the receding horizon scheme. We deal with mathematical models such as state space models of continuous variable systems and controlled Markov chains (CMC) of discrete event systems (DES). For given mathematical models, common design objectives and performance indices are introduced. The advantages of the receding horizon scheme are discussed. In this paper, receding horizon schemes are introduced for both minimization and minimaximization criteria. In the case of state space models, we first start from a general nonlinear system and move to a linear system. Specially, we introduce the state feedback and the output feedback receding horizon controls. A linear time delay and I/O systems are also discussed for applicability of the receding horizon scheme. As an application to a discrete event system, we introduce receding horizon policies for the average reward criterion and the two person zero sum game of controlled Markov chains. The differences between the receding horizon performance criteria and the infinite horizon ones are represented in terms of the horizon size.