Studying evolutionary dynamics is crucial for epidemiological containment and/or eradication of viral diseases. With recent advancements in genetic sequencing, the spread of viruses can be monitored and sequenced almost in real-time as epidemics unfold, and sophisticated statistical analytical methods allow for the inference of population genetic and evolutionary characteristics directly from epidemiologic and genetic data. In this thesis, I have investigated various evolutionary aspects of the human immunodeficiency virus, the causative agent of AIDS, in the context of (a) within-host evolution of the virus in the emergence of resistance to CCR5 antagonist anti-retroviral agents and (b) between-host global evolutionary dynamics of the virus including an investigation of closely related simian immunodeficiency virus endemic in simian hosts. The main outcomes of my work have been, firstly, the development of a novel computational predictor for determining viral tropism from genetic sequences and a study investigating the efficacy of utilising this approach, and other genotypic methods, for screening patients prior to therapy; secondly, the characterisation of complex within-host mutational pathways and population genetic dynamics that give rise to the emergence of a rare form of resistance to CCR5 antagonists, namely the ability for the virus to utilise antagonist-bound CCR5 coreceptor; thirdly, an investigation of the global spread of HIV-1 group O and a proposed reconciliation of previous attempts to characterise genetic diversity observed which were discordant; and fourthly, en exploratory study comparing differences in rates of intrinsic disorder in both HIV and species-specific SIV, as well as human host genes and homologous simian host genes, and investigating the hypothesis that HIV pathogenicity might be attributable to promiscuous protein-protein interactions facilitated through protein intrinsic disorder. These studies have all highlighted aspects that are collectively important for epidemiological and genomic surveillance of infectious disease, especially in characterising transmission dynamics, monitoring changes and adaptation of viruses. Ultimately, I hope that these contributions will asset the wealth of knowledge that exists in this field, which collectively guides research into the development of new drugs and treatment regimens, as well as guidance on public health measures for control of infectious disease.