Mix-valued logic is a natural generalization of Boolean Logic and k-valued logic. It is a new concept proposed by the authors and their research group. It plays an important role in systems control and related fields, and shows it vivid life. The purpose of the paper is to give a systematic survey on the definition, calculation, and main properties of mix-valued logic, and also to normalize the concepts and notations. Using the semi-tensor product of matrices, this paper introducesthe definition of mix-valued logical operators, its calculations, and its basic properties. Then three applications of mix-valued logic are introduced: (1) dynamic game with finite memory of strategies; (2) solving fuzzy relation equations; (3) dynamic-algebraic Boolean networks.