Magnetorheological elastomers (MREs) are adaptive composite materials in the sense that their mechanical properties are tailored by the applied magnetic field. In this paper we developed both isotropic and anisotropic silicone-rubber-based MREs. We examined the zero-magnetic-field dynamic stiffness and damping along with the magnetic field induced changes (the magnetorheological (MR) effect) for the viscoelastic properties of the MREs by conducting both compression and shear investigations. While the anisotropic MREs exhibited substantial magnetic-field-dependent viscoelastic properties at a medium magnetic field, the isotropic ones showed a negligible MR effect. The magnetic filler structure and concentration, loading frequency, and dynamic strain amplitude were all confirmed to play significant roles in the dynamic mechanical performance of the MREs.