This lecture address the following two key criticisms of the empirical application of revealed preference theory: When the RP conditions do not reject, they do not provide precise predictions; and when they do reject, they do not help characterize the nature of irrationality or the degree/direction of changing tastes. Recent developments in the application of RP theory are shown to have rendered these criticisms unfounded. A powerful test of rationality is available that also provides a natural characterization of changing tastes. Tight bounds on demand responses and on the welfare costs of relative price and tax changes are also available and are shown to work well in practice. (JEL: D11, D12, C14) Stanford, May 2004. I would like to thank the participants at those lectures for their comments. I would also like to acknowledge the input of joint research and discussions with Xiaohong Chen, Dennis Kristensen, Rosa Matzkin, and James Powell. This study is part of the program of research of the ESRC Centre for the Microeconomic Analysis of Public Policy at IFS. The financial support of the ESRC and of the Leverhulme Foundation is gratefully acknowledged. The usual disclaimer applies.