Compared to conventional vapor-compression refrigeration systems, magnetic refrigeration is a promising and potential alternative technology. The magnetocaloric effect (MCE) is used to produce heat and cold sources through a magnetocaloric material (MCM). The material is submitted to a magnetic field with active magnetic regenerative refrigeration (AMRR) cycles. Initially, this effect was widely used for cryogenic applications to achieve very low temperatures. However, this technology must be improved to replace vapor-compression devices operating around room temperature. Therefore, over the last 30 years, a lot of studies have been done to obtain more efficient devices. Thus, the modeling is a crucial step to perform a preliminary study and optimization. In this paper, after a large introduction on MCE research, a state-of-the-art of multi-physics modeling on the AMRR cycle modeling is made. To end this paper, a suggestion of innovative and advanced modeling solutions to study magnetocaloric regenerator is described.