Modern population genetics studies typically involve genome-wide genotyping of individuals from a diverse network of ancestries. An important, unsolved problem is how to formulate and estimate probabilistic models of observed genotypes that allow for complex population structure. We formulate two general probabilistic models, and we propose computationally efficient algorithms to estimate them. First, we show how principal component analysis (PCA) can be utilized to estimate a general model that includes the well-known Pritchard-Stephens-Donnelly mixed-membership model as a special case. Noting some drawbacks of this approach, we introduce a new 'logistic factor analysis' (LFA) framework that seeks to directly model the logit transformation of probabilities underlying observed genotypes in terms of latent variables that capture population structure. We demonstrate these advances on data from the human genome diversity panel and 1000 genomes project, where we are able to identify SNPs that are highly differentiated with respect to structure while making minimal modeling assumptions.