Empowered by modern genotyping and large samples, population structure can be accurately described and quantified even when it only explains a fraction of a percent of total genetic variance. This is especially relevant and interesting for humans, where fine-scale population structure can both confound disease-mapping studies and reveal the history of migration and divergence that shaped our species' diversity. Here we review notable recent advances in the detection, use, and understanding of population structure. Our work addresses multiple areas where substantial progress is being made: improved statistics and models for better capturing differentiation, admixture, and the spatial distribution of variation; computational speed-ups that allow methods to scale to modern data; and advances in haplotypic modeling that have wide ranging consequences for the analysis of population structure. We conclude by outlining four important open challenges: The limitations of discrete population models, uncertainty in individual origins, the incorporation of both fine-scale structure and ancient DNA in parametric models, and the development of efficient computational tools, particularly for haplotype-based methods.If one assumes humans across the globe are a single randomly mating population, it would result in only a 5-15% average error when predicting the proportion of observed heterozygotes at a locus. This closeness to an idealized randomly mating population is one vestige of how little evolutionary time has passed since the common origin of all humans in Africa. The departure from random mating predictions due to population differentiation has a classic quantitative measure, called F ST , which appropriately takes on values of 5-15% in global samples of human populations [1][2][3]. If one zooms in within continental regions of the globe, F ST tends to be even lower, regularly taking values below 1%, a threshold which we use here informally to define "fine-scale structure". A triumph of the large datasets available to contemporary population geneticists is that they allow fine-scale structure to be detected and dissected to reveal population relationships (Figure 1).The reason large datasets allow fine-scale structure to be dissected is a statistical phenomenon [4]. Subtle differences in average pairwise similarity become more apparent as the scale of a dataset increases (Figure 2). For principal component analysis (PCA), Patterson et al. [5] have argued that structure reveals itself much like a phase change in physics; namely if the product of the number of genetic markers (m) and individuals (n) is greater than 1/(F ST 2 ) then structure will be evident. The great fortune of human geneticists is that novel technologies have made it affordable to amass datasets large enough to characterize even very subtle population structure.. CC-BY-NC-ND 4.0 International license peer-reviewed) is the author/funder. It is made available under a The copyright holder for this preprint (which was not . http://dx.doi.org/10.1101/073221 d...