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Climate change affects marine biological processes from genetic to ecosystem levels [1–3]. Recent warming in the northeast Atlantic [4, 5] has caused distributional shifts in some fish species along latitudinal and depth gradients [6, 7], but such changes, as predicted by climate envelope models [8], may often be prevented because population movement requires availability of suitable habitat. We assessed the full impacts of warming on the commercially important European continental shelf fish assemblage using a data-driven Eulerian (grid-based) approach that accommodates spatial heterogeneity in ecological and environmental conditions. We analyzed local associations of species abundance and community diversity with climatic variables, assessing trends in 172 cells from records of >100 million individuals sampled over 1.2 million km² from 1980–2008. We demonstrate responses to warming in 72% of …