We develop a two-sided matching model to analyze collaboration between heterogeneous academics and firms. We consider both horizontal and vertical characteristics, i.e., those related to affinity (e.g., preferences for a type of scientific research) and those related to ability (e.g., capacity to produce high-quality scientific output). We show that the conditions for equilibrium matching in terms of affinity-based characteristics are more complex than those of ability-based characteristics. We build a unique dataset based on the teams of academic researchers and firms that proposed research projects to the UK’s Engineering and Physical Sciences Research Council. Our results are suggestive of positive assortative matching in terms of ability and type while the matching is negative assortative in terms of their interactions. In addition, the most able and the most applied academics are the ones that are more likely to propose collaborative as opposed to non-collaborative projects.