This paper reviews recent developments in the empirical analysis of imperfectly competitive markets highlighting outstanding problems. Some of these problems are econometric. The need for a deeper understanding of the small sample properties of semiparametric estimators and of estimators based on moment inequalities head this list. The modeling problems go back to issues which have been a central part of ongoing research programs in economic theory for some time. We consider ways in which applied work can cope with these problems and, in so doing, also inform theory. The use of estimators based on moment inequalities opens up several possiblities in this regard, and the paper looks in detail at the assumptions that have been used to rationalize these estimators and their likely relevance. ∗This is a revised version of my Fisher-Schultz Lecture which was presented at the World Congress of the Econometric Society in London, August 2005. The paper draws extensively from past interactions with my students and coauthors, and I would like to take this opporunity to express both my intellectual debt and my thanks to them. I like to think they enjoyed the experience as much as I did, though that might have been harder for the students in the group. For help on this paper I owe a particular debt to Robin Lee, and to my theory colleagues for helping me to come to terms with parts of their literature. Financial support from the NSF and the Tolousse Network for Information Technologies is greatly appreciated. The word “theory” in the title refers to both economic and econometric theory.