Abstract Most emerging and re-emerging infectious diseases stem from viruses that naturally circulate in non-human vertebrates. When these viruses cross over into humans, they can cause disease outbreaks and epidemics. While zoonotic host jumps have been extensively studied from an ecological perspective, little attention has gone into characterising the evolutionary drivers and correlates underlying these events. To address this gap, we harnessed the entirety of publicly available viral genomic data, employing a comprehensive suite of network and phylogenetic analyses. We address a series of questions concerning the evolutionary mechanisms underpinning viral host jumps. Notably, we challenge conventional assumptions about the directionality of host jumps, demonstrating that humans are as much a source as a sink for viral spillover events, insofar we infer more viruses to have jumped from humans to other animals, than from animals to humans. Moreover, we demonstrate heightened evolution in viral lineages that involve putative host jumps. We further observe that the mutational threshold associated with a host jump is lower for viruses with broad host ranges. Finally, we show that the genomic targets of natural selection upon a successful host jump vary across different viral families with either structural or auxiliary genes being the prime targets of selection. Collectively, our results illuminate some of the evolutionary drivers underlying viral host jumps that may contribute to mitigating viral threats across species boundaries.