Structural variants (SVs) are a numerous and inadequately characterized source of human genetic variation that occur from a diverse set of molecular mechanisms. They include large deletions, duplications, inversions, mobile element insertions (MEIs), and more. Using our state-of-the-art SV calling pipeline, GATK-SV, we have identified over 1.1 million high quality SVs from 63,046 unrelated individuals with whole genome sequencing (WGS) data, newly released as part of the Genome Aggregation Database (gnomAD). Within the gnomAD v4 callset, we identify over 200,000 MEIs, comprising 173,374 Alu, 30,223 L1, and 17,607 SINE-VNTR-Alu (SVA) element insertions, the largest high-quality callset of MEIs released to date. We examined distributional patterns of MEIs across the genomes and gene content, as well as their frequency within different functional annotation categories. We also identified variant distributions within many different sets of noncoding annotations from numerous sources. Additionally, we use the GATK-SV variant calls within the newest release of the GTEx dataset, which consists of paired WGS and transcriptome data from 851 individuals across 54 tissues. Upon identifying expression and splicing quantitative trait loci, we put forth the largest set of common MEIs that are likely causal for changes in expression and splicing.