With the continuous development of time and technology, the control system has thus evolved in the direction of great complexity. In the field of path control, once control algorithms cannot absolutely meet the requirements of all people, so this paper introduces an alternative algorithm-MPC. This article focuses on the development of MPC from when it is invented and its application in aerospace today with specified examples, and then lists and analyses the mainstream MPC algorithms, namely LTI, LTV, LPV, PWA and nonlinear systems. Article below also illustrates the derivation of sample of non-parametric model-based algorithms (Dynamic matrix control) and parametric model-based algorithms (Generalized Predictive Control) and the elaboration of mainstream systems and their applications in the form of an overview. Eventually gives a conclusion to the current situation of MPC and relationships among various algorithms. Note that this article is mainly aimed at scholars who are new to MPC algorithms.