Households' and firms' subjective inflation expectations play a central role in macroeconomic and intertemporal microeconomic models. We discuss how subjective inflation expectations are measured, the patterns they display, their determinants, and how they shape households' and firms' economic choices in the data and help us make sense of the observed heterogeneous reactions to business-cycle shocks and policy interventions. We conclude by highlighting the relevant open questions and why tackling them is important for academic research and policy making.