Aluminum (Al) and copper (Cu) have been widely used in many industrial fields thanks to their good plasticity, high thermal conductivity and excellent electrical conductivity. An effective joining of dissimilar Al and Cu materials can make full use of the special characteristics of these two metals. Friction stir spot welding (FSSW), as an efficient solid-state welding method suitable for joining of dissimilar metal materials, has great prospects in future industrial applications. In this paper, the FSSW studies on Al-Cu dissimilar materials are reviewed. The research progress and current status of Al-Cu FSSW are reviewed with respect to tool features, macroscopic characteristics of welded joints, microstructures, defects in welds and mechanical properties of joints. In addition, some suggestions on further study are put forward in order to promote the development and progress of Al-Cu FSSW studies in several respects: material flow, thermal history, addition of intermediate layer, auxiliary methods and functionalization of Al-Cu FSSW joint.