Genome sequence data provide rich overlays of information on viral evolutionary history with wide temporal scope. When structured with meta-data such as time of sampling, sequence data can even be used to co-estimate key evolutionary and epidemiological dynamics for diverse sets of viruses. Over evolutionary time, genetic variation accumulates in populations through the effect of evolutionary processes, such as mutation, recombination, and reassortment, with variations spread by both stochastic and deterministic mechanisms. These evolutionary processes, and thus the history of a population, can be inferred by analysing and comparing nucleotide sequences sampled from that population. Both comparative studies between viruses and characterisation of specific viruses allow us to develop models within the larger context of evolutionary knowledge of viruses, structuring future theoretical developments and understandings. Improvements in high-throughput sequencing methods means that genomic data is accumulating at a rapid rate, such that large comparative studies are increasing in their power to ascertain evolutionary histories. In this thesis I conduct detailed investigations into the evolutionary history of certain viruses using both established and emerging frameworks, and from these make inferences on the epidemiological dynamics of those viruses.