Inferring the past demography of human populations has been classically approached through data from the archaeological record but more recently by the use of genetic data from contemporary samples. Building realistic demographic models at the continental scale is a necessary step toward the improvement of current genomic methods aimed at finding genes under selection. In light of recent advances in Bayesian statistical inference, we discuss here the importance of considering spatially explicit approaches for modeling population expansion and dispersal. Neutral processes, such as the surfing phenomenon, that occur at the front of a range expansion may indeed mimic selection, and they may have played a significant role in spreading particular alleles over large geographic areas. Finally, we discuss a few important issues that require further investigation, notably the use of archaeological data to inform population genetic models, the simulation of range contraction and reexpansion, and the importance of long-distance dispersal.