Magnesium alloys, renowned for their lightweight yet high-strength characteristics, with exceptional mechanical properties, are highly coveted for numerous applications. The emergence of magnesium alloy additive manufacturing (Mg AM) has further propelled their popularity, offering advantages such as unparalleled precision, swift production rates, enhanced design freedom, and optimized material utilization. This technology holds immense potential in fabricating intricate geometries, complex internal structures, and performance-tailored microstructures, enabling groundbreaking applications. In this paper, we delve into the core processes and pivotal influencing factors of the current techniques employed in Mg AM, including selective laser melting (SLM), electron beam melting (EBM), wire arc additive manufacturing (WAAM), binder jetting (BJ), friction stir additive manufacturing (FSAM), and indirect additive manufacturing (I-AM). Laser powder bed fusion (LPBF) excels in precision but is limited by a low deposition rate and chamber size; WAAM offers cost-effectiveness, high efficiency, and scalability for large components; BJ enables precise material deposition for customized parts with environmental benefits; FSAM achieves fine grain sizes, low defect rates, and potential for precision products; and I-AM boasts a high build rate and industrial adaptability but is less studied recently. This paper attempts to explore the possibilities and challenges for future research in AM. Among them, two issues are how to mix different AM applications and how to use the integration of Internet technologies, machine learning, and process modeling with AM, which are innovative breakthroughs in AM.