Plant roots have greatly diversified in form and function since the emergence of the first land plants, but the global organization of functional traits in roots remains poorly understood. Here we analyse a global dataset of 10 functionally important root traits in metabolically active first-order roots, collected from 369 species distributed across the natural plant communities of 7 biomes. Our results identify a high degree of organization of root traits across species and biomes, and reveal a pattern that differs from expectations based on previous studies of leaf traits. Root diameter exerts the strongest influence on root trait variation across plant species, growth forms and biomes. Our analysis suggests that plants have evolved thinner roots since they first emerged in land ecosystems, which has enabled them to markedly improve their efficiency of soil exploration per unit of carbon invested and to reduce their dependence on symbiotic mycorrhizal fungi. We also found that diversity in root morphological traits is greatest in the tropics, where plant diversity is highest and many ancestral phylogenetic groups are preserved. Diversity in root morphology declines sharply across the sequence of tropical, temperate and desert biomes, presumably owing to changes in resource supply caused by seasonally inhospitable abiotic conditions. Our results suggest that root traits have evolved along a spectrum bounded by two contrasting strategies of root life: an ancestral 'conservative' strategy in which plants with thick roots depend on symbiosis with mycorrhizal fungi for soil resources and a more-derived 'opportunistic' strategy in which thin roots enable plants to more efficiently leverage photosynthetic carbon for soil exploration. These findings imply that innovations of belowground traits have had an important role in preparing plants to colonize new habitats, and in generating biodiversity within and across biomes.