While the early history of the Phillips curve up to 1975 is well known, less well understood is the post-1975 fork in the road. The left fork developed a theory of policy responses to supply shocks in the context of price stickiness in the non-shocked sector. Its econometric implementation interacts shocks with backward-looking inertia. The right fork approach emphasizes forward-looking expectations that can jump in response to anticipated policy changes. The left fork approach is better suited to explaining the postwar US inflation process, while the right fork approach is essential for understanding behaviour in economies with unstable macroeconomic environments.