The purpose of this paper is to discuss some of the models used in New Monetarist Economics, which is our label for a body of recent work on money, banking, payments systems, asset markets, and related topics. A key principle in New Monetarism is that solid microfoundations are critical for understanding monetary issues. We survey recent papers on monetary theory, showing how they build on common foundations. We then lay out a tractable benchmark version of the model that allows us to address a variety of issues. We use it to analyze some classic economic topics, like the welfare effects of inflation, the relationship between money and capital accumulation, and the Phillips curve. We also extend the benchmark model in new ways, and show how it can be used to generate new insights in the study of payments, banking, and asset markets.