We don't yet know which specific variants are responsible for, e.g., population variation in height, but we expect that they can be found given sufficient statistical power. See Genetic architecture and predictive modeling of quantitative traits.
Genetic variance estimation with imputed variants finds negligible missing heritability for human height and body mass index
Nature Genetics (2015) doi:10.1038/ng.3390
We propose a method (GREML-LDMS) to estimate heritability for human complex traits in unrelated individuals using whole-genome sequencing data. We demonstrate using simulations based on whole-genome sequencing data that ~97% and ~68% of variation at common and rare variants, respectively, can be captured by imputation. Using the GREML-LDMS method, we estimate from 44,126 unrelated individuals that all ~17 million imputed variants explain 56% (standard error (s.e.) = 2.3%) of variance for height and 27% (s.e. = 2.5%) of variance for body mass index (BMI), and we find evidence that height- and BMI-associated variants have been under natural selection. Considering the imperfect tagging of imputation and potential overestimation of heritability from previous family-based studies, heritability is likely to be 60–70% for height and 30–40% for BMI. Therefore, the missing heritability is small for both traits. For further discovery of genes associated with complex traits, a study design with SNP arrays followed by imputation is more cost-effective than whole-genome sequencing at current prices.