Structural variants (SVs) can be important drivers of human adaptation with strong effects, but previous studies have focused primarily on common variants with weak effects. Here, we used large-scale single-molecule long-read sequencing of 320 Tibetan and Han samples, to show that SVs are key drivers of selection under high-altitude adaptation. We expand the landscape of global SVs, apply robust models of selection and population differentiation combining SVs, SNPs and InDels, and use epigenomic analyses to predict driver enhancers, target genes, upstream regulators, and biological functions, which we validate using enhancer reporter and DNA pull-down assays. We reveal diverse Tibetan-specific SVs affecting the cis- and trans-regulatory circuitry of diverse biological functions, including hypoxia response, energy metabolism, lung function, etc. Our study greatly expands the global SV landscape, reveals the central role of gene-regulatory circuitry rewiring in human adaptation, and illustrates the diverse functional roles that SVs can play in human biology.