In recent years, more and more researchers focus on the magnetorheological elastomer (MRE) sandwich beam structures. MR elastomers have a better control performance than that of typical MR fluid. it has extensive applications in the semi-active control of structural vibration. In this paper, the studies on dynamic characteristics of the MRE sandwich beam at home and abroad are reviewed. The review focuses on constitutive models of material, methods of theoretical modeling and experimental analysis of MRE sandwich beam, researches and findings. The latest research results show that the natural frequency of MR sandwich beam can be increased or decreased by controlling the intensity and location of the applied magnetic field. At last, the content of this paper is summarized, and the future research direction in this field is prospected.