Inferring population structure is important for several applications in medical and population genetic studies. However, the output of population structure inference methods can often be challenging to interpret. The goal of this dissertation is to apply population structure inference tools to learn and visualize demographic history and develop statistical methods for interpretable population structure inference. In Chapter 2, I apply population structure inference tools to learn about the genetic history of the Mediterranean island of Sardinia using a new ancient DNA dataset. In Chapter 3, I develop a fast and flexible statistical method and optimization algorithm for inferring and visualizing non-homogeneous patterns of migration using spatially indexed population genetic data. Finally, in Chapter 4, I develop a new Bayesian matrix factorization method and variational inference algorithm for emphasizing shared evolutionary histories when representing population structure. Overall, the work presented in this dissertation aims to provide interpretable representations of population structure which, in turn, give understanding into the underlying demographic factors that shape patterns of genetic variation.