In the first of two reports on FinTech, I review definitions, roots and taxonomies of FinTech, survey studies charting FinTech development, and theoretical approaches to FinTech. Emerging empirical research shows a dynamic growth of FinTech characterized by heterogeneity and diversity. Ecosystems, financial ecologies, and digital platform economies are the most popular approaches to FinTech, and I argue that they can be used fruitfully in combination with more established concepts, such as networks and agglomeration. Overall, I show that FinTech research is in a state of flux concerning concepts and empirics, and highlight the potential of geography to tame the beast.