This paper provides a survey on the recent literature on the new Keynesian Phillips curve: the controversies surrounding its microfoundation and estimation, the approaches that have been tried to improve its empirical fit and the challenges it faces adapting to the open-economy framework. The new Keynesian Phillips curve has been severely criticized for poor empirical dynamics. Suggested improvements involve making some adjustments to the standard sticky price framework, e.g. introducing backwardness and real rigidities, or abandoning the sticky price model and relying on models of inattentiveness, learning or state-dependant pricing. The introduction of openeconomy factors into the new Keynesian Phillips curve complicate matters further as it must capture the nexus between price setting, inflation and the exchange rate. This is nevertheless a crucial feature for any model to be used for inflation forecasting in a small open economy like Iceland.