Abstract Machine learning (ML) applications in Earth and environmental sciences (EES) have gained incredible momentum in recent years. However, these ML applications have largely evolved in ‘isolation’ from the mechanistic, process‐based modelling (PBM) paradigms, which have historically been the cornerstone of scientific discovery and policy support. In this perspective, we assert that the cultural barriers between the ML and PBM communities limit the potential of ML, and even its ‘hybridization’ with PBM, for EES applications. Fundamental, but often ignored, differences between ML and PBM are discussed as well as their strengths and weaknesses in light of three overarching modelling objectives in EES, (1) nowcasting and prediction, (2) scenario analysis, and (3) diagnostic learning. The paper ponders over a ‘coevolutionary’ approach to model building, shifting away from a borrowing to a co‐creation culture, to develop a generation of models that leverage the unique strengths of ML such as scalability to big data and high‐dimensional mapping, while remaining faithful to process‐based knowledge base and principles of model explainability and interpretability, and therefore, falsifiability.

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.

Hydrology is still, and for good reasons, an inexact science, even if evolving hydrological understanding has provided a basis for improved water management for at least the last three millennia. The limitations of that understanding have, however, become much more apparent and important in the last century as the pressures of increasing populations, and the anthropogenic impacts on catchment forcing and responses, have intensified. At the same time, the sophistication of hydrological analyses and models has been developing rapidly, often driven more by the availability of computational power and geographical data sets than any real increases in understanding of hydrological processes. This sophistication has created an illusion of real progress but a case can be made that we are still rather muddling along, limited by the significant uncertainties in hydrological observations, knowledge of catchment characteristics and related gaps in conceptual understanding, particularly of the sub-surface. These knowledge gaps are illustrated by the fact that for many catchments we cannot close the water balance without significant uncertainty, uncertainty that is often neglected in evaluating models for practical applications.