Many questions in economics can be fruitfully analyzed in the framework of matching models. Until recently, empirical work has lagged far behind theory in this area. This review reports on recent developments that have considerably expanded the range of matching models that can be taken to the data. A leading theme is that in such two-sided markets, knowing the observable characteristics of partners alone is not enough to credibly identify the relevant parameters. A combination of richer data and robust, theory-driven restrictions is required. We illustrate this on leading applications. (JEL C57, C78)