We estimate the U.S. New Keynesian Phillips Curve in the time-frequency domain with continuous wavelet tools, to provide an integrated answer to the three most controversial issues on the Phillips Curve. (1) Has the short-run tradeoff been stable? (2) What has been the role of expectations? (3) Is there a long-run tradeoff? First, we find that the short-run tradeoff is limited to some specific episodes and short cycles and that there is no evidence of nonlinearities or structural breaks. Second, households expectations captured trend inflation and were anchored until the Great Recession, but not since 2008. Then, inflation over-reacted to expectations at short cycles. Finally, there is no signi cant long-run tradeoff. In the long-run, inflation is explained by expectations.