As highly integrated circuits continue to advance, accompanied by a growing demand for energy efficiency and weight reduction, materials are confronted with mounting challenges pertaining to thermal conductivity and lightweight properties. By virtue of numerous intrinsic mechanisms, as a result, the thermal conductivity and mechanical properties of the Mg alloys are often inversely related, which becomes a bottleneck limiting the application of Mg alloys. Based on several effective modification methods to improve the thermal conductivity of Mg alloys, this paper describes the law of how they affect the mechanical properties, and clearly indicates that peak aging treatment is one of the best ways to simultaneously enhance an alloy's thermal conductivity and mechanical properties. As the most frequently used Mg alloy, cast alloys exhibit substantial potential for achieving high thermal conductivity. Moreover, recent reports indicate that hot deformation can significantly improve the mechanical properties while maintaining, and potentially slightly enhancing, the alloy's thermal conductivity. This presents a meaningful way to develop Mg alloys for applications in the field of small-volume heat dissipation components that require high strength. This comprehensive review begins by outlining standard testing and prediction methods, followed by the theoretical models used to predict thermal conductivity, and then explores the primary influencing factors affecting thermal conductivity. The review summarizes the current development status of Mg alloys, focusing on the quest for alloys that offer both high thermal conductivity and high strength. It concludes by providing insights into forthcoming prospects and challenges within this field.