This paper examines the concept of inflation persistence in macroeconomic theory. It begins with a definition of persistence, emphasizing the difference between reduced-form and structural persistence. It then examines a number of empirical measures of reduced-form persistence, considering the possibility that persistence may have changed over time. The paper then examines the theoretical sources of persistence, distinguishing "intrinsic" from "inherited" persistence, and deriving a number of analytical results on persistence. It summarizes the implications for persistence from the literatures on "sticky-information" models, learning models, and so-called "trend inflation models," providing some new results throughout.