This paper describes concepts and applications of real-time optimization (RTO) and model predictive control (MPC), which are active areas of research in the systems and control community. At each sampling time of MPC, the system response is predicted and optimized over a nite future. Therefore, RTO is a key component of MPC, particularly for nonlinear systems. In recent years, progresses in numerical algorithms and computing power have been widening application areas of MPC from traditional chemical processes to fast nonlinear mechanical systems. Some software tools have also been developed to automate programming of numerical algorithms for MPC. Symbolic computation is an essential element in automatic code generation for MPC of nonlinear systems with complicated mathematical models.