Earth's biodiversity and carbon uptake by plants, or primary productivity, are intricately interlinked, underlie many essential ecosystem processes, and depend on the interplay among environmental factors, many of which are being changed by human activities. While ecological theory generalizes across taxa and environments, most empirical tests of factors controlling diversity and productivity have been observational, single-site experiments, or meta-analyses, limiting our understanding of variation among site-level responses and tests of general mechanisms. A synthesis of results from ten years of a globally distributed, coordinated experiment, the Nutrient Network (NutNet), demonstrates that species diversity promotes ecosystem productivity and stability, and that nutrient supply and herbivory control diversity via changes in composition, including invasions of non-native species and extinction of native species. Distributed experimental networks are a powerful tool for tests and integration of multiple theories and for generating multivariate predictions about the effects of global changes on future ecosystems.