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This paper is the outcome of a community initiative to identify major unsolved scientific problems in hydrology motivated by a need for stronger harmonisation of research efforts. The procedure involved a public consultation through online media, followed by two workshops through which a large number of potential science questions were collated, prioritised, and synthesised. In spite of the diversity of the participants (230 scientists in total), the process revealed much about community priorities and the state of our science: a preference for continuity in research questions rather than radical departures or redirections from past and current work. Questions remain focused on the process-based understanding of hydrological variability and causality at all space and time scales. Increased attention to environmental change drives a new emphasis on understanding how change propagates across interfaces within the hydrological system and across disciplinary boundaries. In particular, the expansion of the human footprint raises a new set of questions related to human interactions with nature and water cycle feedbacks in the context of complex water management problems. We hope that this reflection and synthesis of the 23 unsolved problems in hydrology will help guide research efforts for some years to come. ARTICLE HISTORY

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This paper traces two decades of neural network rainfall-runoff and streamflow modelling, collectively termed ‘river forecasting’. The field is now firmly established and the research community involved has much to offer hydrological science. First, however, it will be necessary to converge on more objective and consistent protocols for: selecting and treating inputs prior to model development; extracting physically meaningful insights from each proposed solution; and improving transparency in the benchmarking and reporting of experimental case studies. It is also clear that neural network river forecasting solutions will have limited appeal for operational purposes until confidence intervals can be attached to forecasts. Modular design, ensemble experiments, and hybridization with conventional hydrological models are yielding new tools for decision-making. The full potential for modelling complex hydrological systems, and for characterizing uncertainty, has yet to be realized. Further gains could also emerge from the provision of an agreed set of benchmark data sets and associated development of superior diagnostics for more rigorous intermodel evaluation. To achieve these goals will require a paradigm shift, such that the mass of individual isolated activities, focused on incremental technical refinement, is replaced by a more coordinated, problem-solving international research body.