The prospect of identifying high-risk viruses and designing interventions to pre-empt their emergence into human populations is enticing, but controversial, particularly when used to justify large-scale virus discovery initiatives. We review the current state of these efforts, identifying three broad classes of predictive models that have differences in data inputs that define their potential utility for triaging newly discovered viruses for further investigation. Prospects for model predictions of public health risk to guide preparedness depend not only on computational improvements to algorithms, but also on more efficient data generation in laboratory, field and clinical settings. Beyond public health applications, efforts to predict zoonoses provide unique research value by creating generalisable understanding of the ecological and evolutionary factors that promote viral emergence.