Changing hydrological conditions due to climate, land use and infrastructure pose significant ongoing challenges to the hydrological research and water management communities. While, traditionally, hydrological models have assumed stationary conditions, there has been much progress since 2005 on model parameter estimation under unknown or changed conditions and on techniques for modelling in those conditions. There is an analogy between extrapolation in space (termed Prediction in Ungauged Basins, PUB), and extrapolation in time (termed Prediction in Ungauged Climates, PUC) that can be exploited for estimating model parameters. Methods for modelling changing hydrological conditions need to progress beyond the current scenario approach, which is reliant upon precalibrated models. Top-down methods and analysis of spatial gradients of a variable of interest, instead of temporal gradients (a method termed ‘Trading space for time’) show much promise for validating more complex model projections. Understanding hydrological processes and how they respond to change, along with quantification of parameter estimation and modelling process uncertainty will continue to be active areas of research within hydrology. Contributions from these areas will not only help inform future climate change impact studies about what will change and by how much, but also provide insight into why any changes may occur, what changes we are able to predict in a realistic manner, and what changes are beyond the current predictability of hydrological systems.