Handbook of the Economics of Matching, Volume Two summarizes both classic results and the many recent advances on matching without transfers. Its seven chapters, written by leading researchers, cover both theoretical and empirical work and include sections on Matching under Non-transferable Utility: Theory, Empirical Approaches to Climate Change Impact Quantification, The large markets case, Matching under Non-transferable Utility: Applications, Allocating students to schools: theory and empirical methods, Matching with contracts, Matching with frictions, and Dynamic Matching.