Adaptation is often thought to affect the likelihood that a virus will be able to successfully emerge in a new host species. If so, surveillance for genetic markers of adaptation could help to predict the risk of disease emergence. However, adaptation is difficult to distinguish conclusively from the other processes that generate genetic change. In this Review we survey the research on the host jumps of influenza A, severe acute respiratory syndrome-coronavirus, canine parvovirus and Venezuelan equine encephalitis virus to illustrate the insights that can arise from combining genetic surveillance with microbiological experimentation in the context of epidemiological data. We argue that using a multidisciplinary approach for surveillance will provide a better understanding of when adaptations are required for host jumps and thus when predictive genetic markers may be present.