This paper shows that a simple form of nonlinearity in the Phillips curve can explain why, following the Great Recession, inflation did not decrease as much as predicted by linear Phillips curves, a phenomenon known as the missing disinflation. We estimate a piecewise-linear specification and document that the data favor a model with two regions, with the response of inflation to an increase in unemployment slower in the region where unemployment is already high. Nonlinearities remain important, even when we account for other factors proposed in the literature, such as consumer expectations of inflation or financial frictions. However, studying a range of specifications with different measures of inflation and economic activity, we conclude that, in most cases, consumer expectations are more robust than nonlinearities. We find that the role of consumer expectations was especially important in the 1970s and ’80s, during a turbulent rise in inflation followed by the Volcker disinflation; the nonlinearities make disinflation more problematic and require the inflation expectations process to be more forward-looking during this period, thereby putting a larger weight on survey expectations. We conclude that a nonlinear Phillips curve with forward-looking survey expectations can be a useful tool to understand inflation dynamics during episodes of rapid disinflation and persistent inflation.