Emerging infectious diseases are often characterised by host-switching events in which a pathogen jumps from its original host to infect a novel species. With changes in land use and increased urbanisation, the frequency with which pathogens jump species barriers to emerge in new hosts is expected to rise. Nevertheless, most emerging infections in humans result in dead-end ‘spillover’ events in which a pathogen is transmitted from an animal reservoir to a human but is unable to achieve the sustained human-to-human transmission necessary for a full-blown epidemic. This talk will focus on my research into the evolutionary processes that might allow novel pathogens to adapt to new hosts; and the potential barriers to host adaptation. First, to better understand the determinants of host adaptation and emergence, I will present a model of key aspects of pathogen evolutionary dynamics at both intra- and inter-host scales. Second, using multivariate modelling and multimodel inference, I will identify those biological features of viruses that best determine inter-human transmissibility. Finally, I will present a comparative co-phylogenetic analysis, which aims to understand how viruses and their hosts co-evolve and reveal the nature of virus macroevolution.