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Abstract Grass species (family Poaceae) are globally distributed, adapted to a wide range of climates and express a diversity of functional strategies. We explored the functional strategies of grass species using the competitor, stress tolerator, ruderal (CSR) system and asked how a species’ strategy relates to its functional traits, climatic distribution and propensity to become naturalized outside its native range. We used a global set of trait data for grass species to classify functional strategies according to the CSR system based on leaf traits. Differences in strategies in relation to lifespan (annual or perennial), photosynthetic type (C3 or C4), or naturalisation (native or introduced) were investigated. In addition, correlations with traits not included in the CSR classification were analyzed, and a model was fitted to predict a species’ average mean annual temperature and annual precipitation across its range as a function of CSR scores. Values for competitiveness were higher in C4 species than in C3 species, values for stress tolerance were higher in perennials than in annuals, and introduced species had more pronounced competitive-ruderal strategies than native species. Relationships between the CSR classification, based on leaf traits, and other functional traits were analyzed. Competitiveness was positively correlated with height, while ruderality was correlated with specific root length, indicating that both above- and belowground traits underlying leaf and root economics contribute to realized CSR strategies. Further, relationships between climate and CSR classification showed that species with competitive strategies were more common in warm climates and at high precipitation, whereas species with stress tolerance strategies were more common in cold climates and at low precipitation. The findings presented here demonstrate that CSR classification of functional strategies based on leaf traits matches expectations for the adaptations of grass species that underlie lifespan, photosynthetic type, naturalization and climate.