Biodegradable magnesium (Mg) alloy stents are the most promising next generation of bio-absorbable stents. In this article, we summarized the progresses on the in vitro studies, animal testing and clinical trials of biodegradable Mg alloy stents in the past decades. These exciting findings led us to propose the importance of the concept “bio-adaption” between the Mg alloy stent and the local tissue microenvironment after implantation. The healing responses of stented blood vessel can be generally described in three overlapping phases: inflammation, granulation and remodeling. The ideal bio-adaption of the Mg alloy stent, once implanted into the blood vessel, needs to be a reasonable function of the time and the space/dimension. First, a very slow degeneration of mechanical support is expected in the initial four months in order to provide sufficient mechanical support to the injured vessels. Although it is still arguable whether full mechanical support in stented lesions is mandatory during the first four months after implantation, it would certainly be a safety design parameter and a benchmark for regulatory evaluations based on the fact that there is insufficient human in vivo data available, especially the vessel wall mechanical properties during the healing/remodeling phase. Second, once the Mg alloy stent being degraded, the void space will be filled by the regenerated blood vessel tissues. The degradation of the Mg alloy stent should be 100% completed with no residues, and the degradation products (e.g., ions and hydrogen) will be helpful for the tissue reconstruction of the blood vessel. Toward this target, some future research perspectives are also discussed.