This lecture covers the dynamic characterization and constitutive behaviors of Magnetorheological Elastomers (MREs). It explores the static and dynamic properties of MREs, the applied magnetic flux density, the strain amplitude, and the strain rate. The lecture delves into the comprehensive investigations to explain the modulus change and examine the material property, as well as the characterization of the constitutive behavior of MREs. It also discusses the dynamic behavior under compressive loading, shear loading, and high strain rate behavior. Various studies and models related to compression properties, magnetic field effects, and strain amplitude are presented, along with experimental results and future research directions.