Three classes of inflation models are discussed: Standard Phillips curves, New Keynesian Phillips curves and Incomplete Competition models. Their relative merits in explaining and forecasting inflation are investigated theoretically and empirically. We establish that Standard Phillips-curve forecasts are robust to types of structural breaks that harm the Incomplete Competion model forecasts, but exaggerate forecast uncertainty in periods with no breaks. As the potential biases in after-break forecast errors for the Incomplete Competition model can be remedied by intercept corrections, it offers the best prospect of successful inflation forecasting.