Zoonotic disease surveillance is typically triggered after animal pathogens have already infected humans. Are there ways to identify high-risk viruses before they emerge in humans? If so, then how and where can identifications be made and by what methods? These were the fundamental questions driving a workshop to examine the future of predictive surveillance for viruses that might jump from animals to infect humans. Virologists, ecologists and computational biologists from academia, federal government and non-governmental organizations discussed opportunities as well as obstacles to the prediction of species jumps using genetic and ecological data from viruses and their hosts, vectors and reservoirs. This workshop marked an important first step towards envisioning both scientific and organizational frameworks for this future capability. Canine parvoviruses as well as seasonal H3N2 and pandemic H1N1 influenza viruses are discussed as exemplars that suggest what to look for in anticipating species jumps. To answer the question of where to look, prospects for discovering emerging viruses among wildlife, bats, rodents, arthropod vectors and occupationally exposed humans are discussed. Finally, opportunities and obstacles are identified and accompanied by suggestions for how to look for species jumps. Taken together, these findings constitute the beginnings of a conceptual framework for achieving a virus surveillance capability that could predict future species jumps.