Background: Genome-wide association studies (GWAS) have largely focused on European descent populations, and the transferability of these findings to diverse populations is dependent on many factors, including selection, genetic divergence, heritability, and phenotype complexity. As medical genomics studies become increasingly large and ethnically diverse, gaining clear insight into population history and genetic diversity from available reference panels is critically important. Results: We disentangle the population history of the widely-used 1000 Genomes Project reference panel, with an emphasis on underrepresented Hispanic/Latino and African descent populations. By leveraging haplotype sharing, linkage disequilibrium decay, and ancestry deconvolution along chromosomes in admixed populations, we gain insights into ancestral allele frequencies, the origins, rates, and timings of admixture, and sex-biased demography. We make empirical observations to evaluate the impact of population structure in association studies, with conclusions that inform rare variant association in diverse populations, how we use standard GWAS tools, and transferability of findings across populations. Finally, we show through coalescent simulations that inferred polygenic risk scores derived from European GWAS are biased when applied to diverse populations. Conclusions: Our study provides fine-scale insight into the sampling, genetic origins, divergence, and sex-biased history of admixture in the 1000 Genomes Project populations. We show that the transferability of results from GWAS are dependent on the ancestral diversity of the study cohort as well as the phenotype polygenicity, causal allele frequency divergence, and heritability. This work highlights the need for inclusion of more diverse samples in medical genomics studies to enable broadly applicable disease risk information.