refrigeration technology. It has been considered as one of promising alternatives to traditional vapor compression refrigeration technology. Magnetic refrigeration, in which solid magnetic materials instead of gaseous refrigerants are used, is based on the magnetocaloric effect. When magnetocaloric material moves in or out of magnetic field, it releases heat due to magnetization or absorbs heat due to demagnetization, respectively. In this paper, magnetocaloric effects (MCEs) and basic thermodynamic cycles are briefly described at first. Some typical magnetic refrigeration cycles are introduced from the viewpoint of thermodynamics, which include hybrid cycle, cycle based on the active magnetic regenerator and cycle based on the active magnetic regenerator coupled with gas regenerative refrigeration. Specifically, magnetic refrigeration cycle based on the active magnetic regenerator (AMR) coupled with gas regenerative refrigeration is a novel idea that combines the magnetocaloric effect with the regenerative gas expansion refrigeration. And it has been under the way to try to achieve greater refrigeration performance of the coupled refrigerator in the research institutions. Thereafter, the paper reviews the existing different numerical models of AMR refrigerator. Analyzing and optimizing an AMR magnetic refrigerator are typical complicated multi-physics problems, which include heat transfer, fluid dynamics and magnetics. The majority of models published are based on one-dimensional simplification, which requires shorter computation time and lower computation resources. Because a one-dimensional model idealizes many factors important for the system performance, two- or three- dimensional numerical models have been setup. Besides, some key items for the model are described in detail, such as magnetocaloric effect, thermal conduction, thermal losses, demagnetizing effect and magnetic hysteresis. Considering the accuracy, convergence and computation time, it is quite vital for numerical models to choose some influential factors reasonably. Then, the recent typical room magnetic refrigeration systems are listed and grouped into four types, i.e., reciprocating-magnet type, reciprocating-regenerator type, rotary-magnet type, and rotaryregenerators type. Different characteristics of these four types are compared. Reciprocating magnetic refrigerators have the advantages of simple construction and max magnetic field intensity difference. Rotary magnetic refrigerator due to compact construction, higher operational frequency and better performance is deemed as a more promising type, in the progress of magnetic refrigeration technology. Meanwhile there are still some key challenges in the practical implementation of magnetic refrigeration technology, such as the development and preparation technologies of high-performance MCE materials, powerful magnetic circuit system and flowing condition. Finally, possible applications are discussed and the tendency of future development is given.