Structural variants (SVs) rearrange large segments of DNA1 and can have profound consequences in evolution and human disease2,3. As national biobanks, disease-association studies, and clinical genetic testing have grown increasingly reliant on genome sequencing, population references such as the Genome Aggregation Database (gnomAD)4 have become integral in the interpretation of single-nucleotide variants (SNVs)5. However, there are no reference maps of SVs from high-coverage genome sequencing comparable to those for SNVs. Here we present a reference of sequence-resolved SVs constructed from 14,891 genomes across diverse global populations (54% non-European) in gnomAD. We discovered a rich and complex landscape of 433,371 SVs, from which we estimate that SVs are responsible for 25-29% of all rare protein-truncating events per genome. We found strong correlations between natural selection against damaging SNVs and rare SVs that disrupt or duplicate protein-coding sequence, which suggests that genes that are highly intolerant to loss-of-function are also sensitive to increased dosage6. We also uncovered modest selection against noncoding SVs in cis-regulatory elements, although selection against protein-truncating SVs was stronger than all noncoding effects. Finally, we identified very large (over one megabase), rare SVs in 3.9% of samples, and estimate that 0.13% of individuals may carry an SV that meets the existing criteria for clinically important incidental findings7. This SV resource is freely distributed via the gnomAD browser8 and will have broad utility in population genetics, disease-association studies, and diagnostic screening.