This paper has been prepared for an invited lecture delivered by Kojima at the 2010 Annual Meeting of the Japanese Economic Association. A large part of this survey is based on Kojima (2009) and Kojima and Yasuda (2009, 2010) as well as lecture notes from Kojima's lectures (regular classes and mini-lectures) at Princeton, Stanford, Tokyo, Yale, and Yonsei. We are grateful to Mutafa Oguz Afacan and Tarun Galagali for their research assistance.
This paper provides a survey of the research in matching and market design. We discuss both basic theories and recent advances. Emphasis is placed on applications of the theory to practical problems.