Magnetic refrigeration is a new environmentally benign technology and a promising alternative to conventional vapor-cycle refrigeration. Among these technologies the household refrigerator without a freezing compartment shows very good prospects for a successful application. This article starts with the general principle of magnetic refrigeration and then also describes the maximum specific cooling capacity of magneto caloric materials. The specific cooling power of a magnetocaloric material is found to be large even for medium magnetic field changes, especially if the frequency is not too small. For a domestic magnetic refrigerator, a comparison with a standard compressor refrigerator is presented. The modeling of a rotary magnetic refrigerator is described and its dynamic behavior is investigated. The physical model is based on a mapping of the magneto-thermodynamic problem from a cylinder onto two rectangles. In this model, in a basic centre cell, two coupled linear partial differential equations are solved, which have been programmed in the Modelica language. Steady-state solutions are envisaged to determine the coefficient of performance, COP, for these conditions. In future work the developed model shall be applied for an optimization of the magnetic refrigerator and to determine the related best parameters.