Magnesium alloys, which are the lightest structural alloys and have a density that is around one-fourth that of steel, present tremendous potential for increasing the energy efficiency of the automobile and aerospace industries. Research on welding magnesium alloys has also increased rapidly as can be seen from journal publications. However, during the welding process, magnesium alloys are highly susceptible to solidification cracking, which prevents their usage in safety–critical applications. The article summarizes and reviews the research progress on solidification cracking of magnesium alloys during welding. The metallurgical and mechanical factors influencing solidification cracking of magnesium alloys are the primary areas of focus in this work. Models and methods for predicting solidification cracking susceptibility of magnesium alloys during welding was developed. More interesting findings on the liquid backfilling to heal cracks and effect of weld pool on solidification cracking were pointed out. The remedies to reduce solidification cracking during welding magnesium alloys were also reviewed so as to achieve high-quality welding and widen the application of magnesium alloys. Graphical Abstract