The rheological properties of magnetorheological (MR) materials, such as their viscosity and dynamic modulus, can be tuned or controlled by changing the intensity of the magnetic field using appropriate control schemes. Thanks to their robustness, performance and smart properties, numerous studies have been undertaken on the development of new MR materials, and microscopic and macroscopic modelling approaches. Novel applications include engine mounts and clutch systems in the automotive industry, shock absorbing safety devices for cockpit seats in aerospace, and shock absorption from movement in semi-active human prosthetic legs.