Magnesium and its alloys, as a promising class of materials, is popular in lightweight application and biomedical implants due to their low density and good biocompatibility. Additive manufacturing (AM) of Mg and its alloys is of growing interest in academia and industry. The domain-by-domain localized forming characteristics of AM leads to unique microstructures and performances of AM-process Mg and its alloys, which are different from those of traditionally manufactured counterparts. However, the intrinsic mechanisms still remain unclear and need to be in-depth explored. Therefore, this work aims to discuss and analyze the possible underlying mechanisms regarding defect appearance and elimination, microstructure formation and evolution, and performance improvement, based on presenting a comprehensive and systematic review on the relationship between process parameters, forming quality, microstructure characteristics and resultant performances. Lastly, some key perspectives requiring focus for further progression are highlighted to promote development of AM-processed Mg and its alloys and accelerate their industrialization.