We survey literature comparing inflation targeting (IT) and price‐level targeting (PT) as macroeconomic stabilisation policies. Our focus is on New Keynesian models and areas that have seen significant developments since Ambler's (2009, Price‐level targeting and stabilisation policy: a survey. Journal of Economic Surveys 23(5): 974–997) survey: optimal monetary policy; the zero lower bound; financial frictions and transition costs of adopting a PT regime. Ambler's conclusion that PT improves social welfare in New Keynesian models is fairly robust, but we note an interesting split in the literature: PT consistently outperforms IT in models where policymakers commit to simple Taylor‐type rules, but results in favour of PT when policymakers minimise loss functions are overturned with small deviations from the baseline model. Since the beneficial effects of PT appear to hang on the joint assumption that agents are rational and the economy New Keynesian, we discuss survey and experimental evidence on rational expectations and the applied macro literature on the empirical performance of New Keynesian models. Overall, the evidence is not clear‐cut, but we note that New Keynesian models can pass formal statistical tests against macro data and that models with rational expectations outperform those with behavioural expectations (i.e. heuristics) in direct statistical tests. We therefore argue that policymakers should continue to pay attention to PT.