Dissimilar material joints of steel and aluminium alloys offer a very high application potential, particularly for lightweight construction. For this material combination, laser beam brazing and laser beam welding are highly automatable as well as established processes and are of great interest, and thus currently a topic of research. Several current research approaches by the Laser Zentrum Hannover e. V. are introduced in the following article, after giving a short overview of the fundamental physical problems in thermally joining the two materials.