The critical step in the emergence of a new epidemic or pandemic viral pathogen occurs after it infects the initial spillover host and then is successfully transmitted onwards, causing an outbreak chain of transmission within that new host population. Crossing these choke points sets a pathogen on the pathway to epidemic emergence. While many viruses spill over to infect new or alternative hosts, only a few accomplish this transition-and the reasons for the success of those pathogens are still unclear. Here, we consider this issue related to the emergence of animal viruses, where factors involved likely include the ability to efficiently infect the new animal host, the demographic features of the initial population that favour onward transmission, the level of shedding and degree of susceptibility of individuals of that population, along with pathogen evolution favouring increased replication and more efficient transmission among the new host individuals. A related form of emergence involves mutations that increased spread or virulence of an already-known virus within its usual host. In all of these cases, emergence may be due to altered viral properties, changes in the size or structure of the host populations, ease of transport, climate change or, in the case of arboviruses, to the expansion of the arthropod vectors. Here, we focus on three examples of viruses that have gained efficient onward transmission after spillover: influenza A viruses that are respiratory transmitted, HIV, a retrovirus, that is mostly blood or mucosal transmitted, and canine parvovirus that is faecal:oral transmitted. We describe our current understanding of the changes in the viruses that allowed them to overcome the barriers that prevented efficient replication and spread in their new hosts. We also briefly outline how we could gain a better understanding of the mechanisms and variability in order to better anticipate these events in the future. This article is part of the theme issue Dynamic and integrative approaches to understanding pathogen spillover.