Lung-function impairment underlies chronic obstructive pulmonary disease (COPD) and predicts mortality. In the largest multi-ancestry genome-wide association meta-analysis of lung function to date, comprising 588,452 participants, we identified 1,020 independent association signals implicating 559 genes supported by ≥2 criteria from a systematic variant-to-gene mapping framework. These genes were enriched in 29 pathways. Individual variants showed heterogeneity across ancestries, age and smoking groups, and collectively as a genetic risk score showed strong association with COPD across ancestry groups. We undertook phenome-wide association studies for selected associated variants as well as trait and pathway-specific genetic risk scores to infer possible consequences of intervening in pathways underlying lung function. We highlight new putative causal variants, genes, proteins and pathways, including those targeted by existing drugs. These findings bring us closer to understanding the mechanisms underlying lung function and COPD, and should inform functional genomics experiments and potentially future COPD therapies.