A statistically significant relationship between the unemployment gap and inflation can be found for a clear majority of OECD countries, but the magnitude of the effect is typically weak. A corollary is that the effect of labour market slack on inflation can often be dominated by other shocks, including imported inflation. The current Secretariat Phillips curve specification assumes inflation expectations are anchored at the central bank’s target, although some experimentation suggests that alternative proxies for expectations sometimes work better and there is some evidence that persistent under-shooting of inflation has led to some de-anchoring of expectations from the target, especially in the euro area. For most OECD countries, a measure of the global output gap is both statistically significant and strongly preferred to a domestic gap measure in explaining the wedge between headline and core inflation, although domestic gaps are strongly preferred in explaining core inflation. Various forms of non-linearity in the Phillips curve provide possible explanations for recent weak inflation outcomes, but statistical testing provides only limited support for such explanations.