Global climate change affects marine fish through drivers such as ocean warming, acidification and oxygen depletion, causing changes in marine ecosystems and socioeconomic impacts. While experimental and observational results can inform about anticipated effects of different drivers, linking between these results and ecosystem-level changes requires quantitative integration of physiological and ecological processes into models to advance research and inform management. We give an overview of important physiological and ecological processes affected by environmental drivers. We then provide a review of available modelling approaches for marine fish, analysing their capacities for process-based integration of environmental drivers. Building on this, we propose approaches to advance important research questions. Examples of integration of environmental drivers exist for each model class. Recent extensions of modelling frameworks increase the potential for including detailed mechanisms and improving model projections. Experimental results on energy allocation, behaviour and physiological limitations will advance the understanding of organism-level trade-offs and thresholds in response to multiple drivers. More explicit representation of life cycles and biological traits can improve description of population dynamics and adaptation, and data on food web topology and feeding interactions help to detail the conditions for possible regime shifts. Identification of relevant processes will also benefit the coupling of different models to investigate spatial–temporal changes in stock productivity and integrated responses of social–ecological systems. Thus, a more process-informed foundation for models will promote the integration of experimental and observational results and increase the potential for model-based extrapolations into a future under changing environmental conditions.