This thesis aims to develop and implement population genetic models that are directly interpretable in terms of events such as population fission and admixture. Two competing methods of approximating the Wright--Fisher model of genetic drift are critically examined, one due to Balding and Nichols and another to Nicholson and colleagues. The model of population structure consisting of all present-day subpopulations arising from a common ancestral population at a single fission event (first described by Nicholson et al.) is reimplemented and applied to single-nucleotide polymorphism data from the HapMap project. This Bayesian hierarchical model is then elaborated to allow general phylogenetic representations of the genetic heritage of present-day subpopulations and the performance of this model is assessed on simulated and HapMap data. The drift model of Balding and Nichols is found to be problematic for use in this context as the need for allele fixation to be modelled becomes apparent. The model is then further developed to allow the inclusion of admixture events. This new model is, again, demonstrated using HapMap data and its performance compared to that of the TreeMix model of Pickrell and Pritchard, which is also critically evaluated.