The research area “Design of Matching Markets” focuses on the analysis and design of markets in which participants care about who they transact with, rather than just about whether a transaction takes place. Hence, prices do not necessarily lead to efficient allocation. Prominent examples include labour markets or the allocation of kindergarten, school and university places, where both sides have to choose each other: students cannot just decide to attend a popular university, they also have to be admitted (and vice versa). A major challenge in these markets is designing allocation mechanisms in a way that all participants have an incentive to reveal their true preferences. This can prevent individual participants from taking advantage of others through strategic reporting of their preferences. At the same time, it facilitates the empirical analysis of existing allocation practices, such as the introduction of gender and minority quotas in labour markets or catchment areas in school choice.