Unlike the widespread applications of algebraic methods in computer science, coalgebraic methods, as the dual concepts of algebras, have not been noticed by computer scientists till the mid 1990s. In algebraic methods, the constructive elements of data types are studied, while in coalgebraic methods, the observable behaviors of systems are investigated. Coalgebraic methods have distinct advantages in mathematic study of state-based systems since them enable the depth research on those systems’ properties such as behavior equivalence, nondeterminism and so on. Coalgebraic methods have also been applied in many research fields, for example, automata theory, semantics of concurrency, specifications of object-oriented software etc. The recent progress of coalgebraic methods, including its basic concepts, categorical foundations, logical foundations and its applications, is summarized for raising the attention of the relative researchers.