Composite materials consisting of rather rigid polymeric matrices filled with magnetic particles have been known for a long time and are called magnetic elastomers or magnetoelasts. These traditional magnetic elastomers have low flexibility and practically do not change their size, shape and elastic properties in the presence of external magnetic field. A new generation of magnetic elastomers represent a new type of composites, consisting of small (mainly nano-sized) magnetic particles dispersed in a high elastic polymeric matrix. The particles couple the shape of the elastomer to the external magnetic fields. The particles can not leave the polymer matrix, so that all of the forces acting on the particles are transmitted directly to the polymer chains resulting in either locomotion or deformation. Shape distortion occurs instantaneously and disappears abruptly when external fields are applied or removed, respectively. Combination of magnetic and elastic properties leads to a number of striking phenomena that are exhibited in response to impressed magnetic fields. The appearance of the unique ability of such materials to change their size and mechanical properties in a reversible manner has inherent interest if for no other reason than the uniqueness of having giant elastic response to magnetic polarization. The giant deformational effect, tunable elastic modulus, non-homogeneous deformation and quick response to magnetic field open new opportunities for using such materials for various applications. Since the magnetic fields are convenient stimuli from the point of view of signal control, therefore it is of great importance to develop and study such flexible magnetic systems for the design of active soft and large motion actuators, tuned vibration absorbers, stiffness tuneable mounts and suspensions.