Welding of dissimilar magnesium alloys and aluminum alloys is an important issue because of their increasing applications in industries. In this document, the research and progress of a variety of welding techniques for joining dissimilar Mg alloys and Al alloys are reviewed from different perspectives. Welding of dissimilar Mg and Al is challenging due to the formation of brittle intermetallic compound (IMC) such as Mg17Al12 and Mg2Al3. In order to increase the joint strength, three main research approaches were used to eliminate or reduce the Mg-Al intermetallic reaction layer. First, solid state welding techniques which have a low welding temperature were used to reduce the IMCs. Second, IMC variety and distribution were controlled to avoid the degradation of the joining strength in fusion welding. Third, techniques which have relatively controllable reaction time and energy were used to eliminate the IMCs. Some important processing parameters and their effects on weld quality are discussed, and the microstructure and metallurgical reaction are described. Mechanical properties of welds such as hardness, tensile, shear and fatigue strength are discussed. The aim of the report is to review the recent progress in the welding of dissimilar Mg and Al to provide a basis for follow-up research.