The extent to which financial technology will shape the banking industry depends in part on the nature of competition for banking services that arises from innovation by incumbent banks and the entry of new players. This paper presents a review of the growing body of economic literature on financial technology and competition for banking services. The review highlights that fintech has spurred innovation and competition across banking services including in payments, lending, deposit taking and advisory services. Research finds that entry by new fintech-based service providers has expanded access to financial services and put pressure on the market share and pricing power of incumbent banks. The evidence also suggests that fintech-based firms that started out as lenders or payments providers have evolved to offer a broader range of services. We cannot fully know how ongoing innovation will affect business models, but so far, the literature highlights some enduring strengths for the model that bundles a variety of banking services in a single firm, ie, a bank.