In this paper, we discuss the modern history of monetarism and its alternatives, as well as the changing empirical relationship of various measures of money and inflation. After demonstrating that previous naïve correlations between money and inflation as established in the 20th century literature have largely disappeared, we explain why this cannot be taken as support for an increased reliance on permanent monetary finance. Rather, we argue that rapid technological innovation in payments systems--both public and private--including in global pledged collateral markets, portends a declining demand for central bank liabilities.