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Demographic forces shaping the genetic variation we observe today can include population divergences, admixture events and continuity through time. The advancement of high-throughput sequencing technologies, together with developments in molecular and bio-informatics methods, mean the number of ancient genomes available for inference has risen steeply. To make effective use of aDNA however, inference tools need to be developed that account for temporal as well as geographic sampling of genomes. Here I have developed, evaluated and applied methods for estimating divergence times between ancient and modern populations. I used simulation to study the sensitivity of these approaches to violations of model assumptions, before applying them to study the history of population divergence between pairs of populations from a global panel. Non-tree-like demography is common in the human past, with evidence of ancestral structure in the form of archaic admixture in the genomes of all non-African modern humans. Using SNP-array data collected from 118 ethnic groups in the Philippines, I show that the highest levels of Denisovan ancestry are found among the Ayta Magbukon, further highlighting the complex history between modern human groups and the archaic hominins occupying Eurasia before our arrival. Among the most important contributions population genetics has made to the study of the human past is the demonstration that cultural transitions and spread of technologies were often associated with migrating groups of people. This can result in the admixture, displacement or replacement of populations, and aDNA provides us with the opportunity to assess these trends directly through time. I developed a statistical tool to detect population continuity through time, evaluating its performance using simulation. Applied to a dataset of ancient genomes from Early Neolithic Scandinavia, I demonstrate population continuity in the hunter-gathering Pitted Ware culture, despite these people overlapping both geographically and temporally with farmers of the Funnel Beaker culture. In another study of the hunter-gatherer ancestors of the San people of southern Africa, I show evidence that this group exhibited long-term population isolation, remaining unaffected by admixture from outside southern Africa until surprisingly recent times. Using these ancient genomes, I provide further evidence that all modern Khoe-San populations exhibit significant levels of admixture with people of non-Khoe-San ancestry, demonstrating the strong impact migrations in this region have had in the past ~2,000 years.