The real exchange rate is said to be the single most important price in an economy. While we used to think that we knew what explained its movements (e.g., the Balassa-Samuelson effect), the recent much-cited result by Engel (1999) proposes a serious reinterpretation i.e., nearly 100% of the movements in the U.S. real exchange rate are explained by deviations from the law of one price. Engels finding holds even in the medium run, when movements in the relative price of non-tradables between countries, were thought to be of paramount importance. In this project, we study the movement of real exchange rates based on the prices of Big Macs (which we show are highly correlated with the CPIbased real exchange rates). Our main innovation is to match these prices to the prices of individual ingredients (ground beef, bread, lettuce, labor cost, rent, etc.) in 34 countries during 19902002. There are a number of advantages associated with our approach. First, unlike the CPI real exchange rate, we can measure the Big Mac real exchange rate in levels in an economically meaningful way. Second, unlike the CPI real exchange rate for which the attribution to tradable and non-tradable components involves assumptions on the weights and the functional form, we (almost) know the exact composition of a Big Mac, and can estimate the tradable and non-tradable components relatively precisely. Third, we can study the dynamics of the real exchange rate in a setting that is free of the productaggregation bias (argued by Imbs, Mumtaz, Ravn, and Rey, 2002, to be important in studies on CPI real exchange rates), the temporal aggregation bias (argued to be important by Taylor, 2001), or the bias generated by non-compatible consumption baskets across countries. Fourth, we show that Engel's result that deviation from the law of one price is all that matters does not hold generally. Furthermore, deviations from his result can be systematically explained.