Social matching systems bring people together in both physical and online spaces. They have the potential to increase social interaction and foster collaboration. However, social matching systems lack a clear intellectual foundation: the nature of the design space, the key research challenges, and the roster of appropriate methods are all ill-defined. This article begins to remedy the situation. It clarifies the scope of social matching systems by distinguishing them from other recommender systems and related systems and techniques. It identifies a set of issues that characterize the design space of social matching systems and shows how existing systems explore different points within the design space. It also reviews selected social science results that can provide input into system design. Most important, the article presents a research agenda organized around a set of claims. The claims embody our understanding of what issues are most important to investigate, our beliefs about what is most likely to be true, and our suggestions of specific research directions to pursue.