Climate change affects marine biological processes from genetic to ecosystem levels . Recent warming in the northeast Atlantic  has caused distributional shifts in some fish species along latitudinal and depth gradients , but such changes, as predicted by climate envelope models , 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 common species, with three times more species increasing in abundance than declining, and find these trends reflected in international commercial landings. Profound reorganization of the relative abundance of species in local communities occurred despite decadal stability in the presence-absence of species. Our analysis highlights the importance of focusing on changes in species abundance in established local communities to assess the full consequences of climate change for commercial fisheries and food security.