We develop a two-sided matching model to analyze collaboration between heterogeneous academics and firms. We predict a positive assortative matching in terms of both scientific ability and affinity for type of research, but negative assortative in terms of ability on one side and affinity in the other. In addition, the most able and most applied academics and the most able and most basic firms shall collaborate rather than stay independent. Our predictions receive strong support from the analysis of the teams of academics and firms that propose research projects to the UK’s Engineering and Physical Sciences Research Council.