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Using both novel and established molecular evolutionary modelling techniques, we have investigated the evolution of primate lentiviruses and interactions with their hosts. Firstly, we studied SAMHD1, a restriction factor of HIV-1 which is neutralised by lentiviral proteins. SAMHD1 has previously been shown to be under positive selection in primates, ostensibly due to pressure to escape recognition by lentiviral antagonists. We show positive selection is not unique to primates but has occurred throughout chordate evolution. In mammals, we unexpectedly find SAMHD1 sites under positive selection are clustered in the domain controlling enzymatic activation. We hypothesise that positive selection is driven by undiscovered animal viruses and/or precise regulation of SAMHD1 activity. Secondly, we analysed the capsid proteins of pandemic HIV-1 and its chimpanzee progenitor, SIVcpz. We looked for sites evolving under different selective constraints with the aim of discovering host specific adaptation. We identify sites in the domain bound by host cofactors, which govern crucial events in virus replication and prevent immune sensing, suggesting host specific responses to cofactor interaction. Thirdly, we apply this same approach to pandemic HIV-1 and SIVcpz accessory proteins, which mitigate host immunity. Surprisingly, we identify sites in regions of nef and vpr involved in putatively conserved interactions with host proteins, suggesting unexpected host specific adaptation. In vpu, we identify sites involved in antagonism of the restriction factor tetherin - a function acquired by pandemic HIV-1 on adaptation to humans - together with sites which we hypothesise are similarly involved. Finally, lentiviruses and other organisms possess overlapping coding sequences, for which existing codon selection models are unsuitable. We propose a novel approach which models nucleotide substitution. In synthetic data tests, one of four candidate models was accurate and we developed a mixture model for identifying positive selection at codon sites, which we also tested with synthetic data.