Financial intermediation has changed dramatically over the past 30 years, due in large part to technological change. The paper first describes the role of the financial system in a modern economy and how technological change and financial innovation can affect social welfare. We then survey the empirical literatures relating to several specific financial innovations, broadly categorized as new production processes, new products or services, or new organizational forms. In each case, we also include examples of significant fintech innovations that are transforming various aspects of banking. Drawing on the literature on innovations from the 1990s and 2000s informs what we might expect from recent developments.