Natural populations, including those of humans, have complex geographies and histories. Studying how they evolve is difficult, but it is possible with population-based DNA sequence data. However, the study of structured populations is divided by two distinct schools of thought and analysis. The phylogeographic approach is fundamentally graphical and begins with a gene-tree estimate. By contrast, the more traditional approach of using summary statistics is fundamentally mathematical. Both approaches have limitations, but there is promise in newer probabilistic methods that offer the flexibility and data exploitation of the phylogeographic approach in an explicitly model-based mathematical framework.