We survey recent literature comparing inflation targeting (IT) and price-level targeting (PT) as macroeconomic stabilization policies. Our focus is on New Keynesian models and areas which have seen significant developments since Ambler's (2009) survey: the zero lower bound on nominal interest rates; financial frictions; and optimal monetary policy. Ambler's main conclusion that PT improves the inflation-output volatility trade-off in New Keynesian models is reasonably robust to these extensions, several of which are attempts to address issues raised by the recent financial crisis. The beneficial effects of PT therefore appear to hang on the joint assumption that agents are rational and the economy New Keynesian. Accordingly, we discuss recent experimental and survey evidence on whether expectations are rational, as well as the applied macro literature on the empirical performance of New Keynesian models. In addition, we discuss a more recent strand of applied literature that has formally tested New Keynesian models with rational expectations. Overall the evidence is not conclusive, but we note that New Keynesian models are able to match a number of dynamic features in the data and that behavioural models of the macroeconomy are outperformed by those with rational expectations in formal statistical tests. Accordingly, we argue that policymakers should continue to pay attention to PT.