A fundamental mystery of the genome-wide association study (GWAS) era is the gap between the heritability of phenotypes observed in family studies and the heritability successfully explained by association studies. One often cited source of this "missing heritability" is structural variants, which account for a majority of the base pairs varying among genomes but are usually omitted in GWAS due to the difficulty of genotyping them. In this talk, I will present new methods that enable the extension of GWAS analyses to a certain class of structural variants, variable number tandem repeats (VNTRs). The methods allow phasing of diploid repeat length estimates in whole-genome sequence data and imputation of repeat variants into much larger genotyped cohorts. I will discuss ongoing efforts to apply this approach genome-wide in UK Biobank (N~500K) and incorporate these variants in association studies.