Studies looking at flood risk analysis and assessment (FRA) reviews are not customary, and they usually approach to methodological and spatial scale issues, uncertainty, mapping or economic damage topics. However, most of these reviews provide a snapshot of the scientific state of the art of FRA that shows only a partial view, focused on a limited number of selected methods and approaches. In this paper, we apply a bibliometric analysis using the Web of Science (WoS) database to assess the historic evolution and future prospects (emerging fields of application) of FRA. The scientific production of FRA has increased considerably in the past decade. At the beginning, US researchers dominated the field, but now they have been overtaken by the Chinese. The Netherlands and Germany may be highlighted for their more complete analyses and assessments (e.g., including an uncertainty analysis of FRA results), and this can be related to the presence of competitive research groups focused on FRA. Regarding FRA fields of application, resilience analysis shows some growth in recent years while land planning, risk perception and risk warning show a slight decrease in the number of papers published. Global warming appears to dominate part of future FRA production, which affects both fluvial and coastal floods. This, together with the improvement of economic evaluation and psycho-social analysis, appear to be the main trends for the future evolution of FRA. Finally, we cannot ignore the increase in analysis using big data analysis, machine learning techniques, and remote sensing data (particularly in the case of UAV sensors data).