Abstract Long-read and strand-specific sequencing technologies together facilitate the de novo assembly of high-quality haplotype-resolved human genomes without parent–child trio data. We present 64 assembled haplotypes from 32 diverse human genomes. These highly contiguous haplotype assemblies (average contig N50: 26 Mbp) integrate all forms of genetic variation across even complex loci such as the major histocompatibility complex. We focus on 107,590 structural variants (SVs), of which 68% are inaccessible by short-read sequencing. We identify new SV hotspots (spanning megabases of gene-rich sequence), characterize 130 of the most active mobile element source elements, and find that 63% of all SVs arise by homology-mediated mechanisms—a twofold increase from previous studies. Our resource now enables reliable graph-based genotyping from short reads of up to 50,340 SVs, resulting in the identification of 1,525 expression quantitative trait loci (SV-eQTLs) as well as SV candidates for adaptive selection within the human population.