Magnetic refrigeration is a kind of energy-saving, environment-friendly and intrinsically-high-efficient refrigeration technology, which has a wide application prospect. At present, the magnetic refrigeration systems based on active magnetic regenerator cycle have been widely studied and many prototypes of refrigerators have been developed. However, fluids and gases are mainly applied to heat exchange in these systems, which brings some problems such as low operating frequency, large regenerative loss, and complicated sub-component design. These problems increase the cost and reduce the efficiency of magnetic refrigerators. In view of the above problems and challenges, researchers try to introduce the solid-state heat transfer enhancement mechanism, and to design and optimize the full-solid-state magnetic refrigeration system model. In this paper, the development process of magnetic refrigeration technology at room temperature is briefly introduced at first. And the reasons for the low operating frequency and efficiency of the magnetic refrigerator, caused by using fluids for heat exchange, are analyzed. Then, two types of solid-state heat exchange media are briefly described, which are thermal diodes (i.e., electric-field-controlled thermal diode and magnetic-field-controlled thermal diode) and high thermal-conductivity material elements. In this paper we review the research progress of the full-solid-state magnetic refrigeration model based on thermal diodes and high thermal-conductivity material elements. Some key items for these models are described in detail, such as the architectural design concept, physical mechanism and working principle, the main performance simulation results of these systems and their physical change rules. Then, the main performances (i.e. operating frequency, specific cooling power, temperature span, and coefficient of performance) of the full-solid-state magnetic refrigeration model and the AMR model are summarized and comparatively analyzed. It shows that the full-solid-state magnetic refrigeration system can work at high frequency and has greater specific-cooling-power. Meanwhile the design of full-solid-state magnetic refrigeration system is more compact and simpler. The characteristics and problems of the two types of solid heat exchange media are also analyzed. Due to the strong thermal transport capability, easy access and integration of thermoelectric elements, the full-solid-state magnetic refrigeration technology based on thermoelectric thermal diodes has greater application potential. Finally, the main research directions and key scientific problems for further studying the full-solid-state magnetic refrigeration field are discussed and analyzed.