Global viral diversity is substantial, but viruses that contribute little to the public health burden or to agricultural damage receive minimal attention until a seemingly unimportant virus becomes a threat. The Zika virus (ZIKV) illustrated this, as there was limited information and awareness of the virus when it was identified as a public health emergency in February 2016. Predicting which virus may pose a future threat is difficult. This is in part because significant knowledge gaps in the basic biology and ecology of an emerging virus can impede policy development, delay decision making, and hinder public health action. We suggest using a phylogenetic framework of pathogens and their infected host species for insight into which animals may serve as reservoirs. For example, examining flaviviruses closely related to ZIKV, the phylogenetic framework indicates New World monkeys are the most likely candidates to be potential reservoirs for ZIKV. Secondarily, mammals that are in close proximity to humans should be considered because of the increased opportunity for pathogen exchange. The increase in human-mediated environmental change is accelerating the probability of another previously overlooked virus becoming a significant concern. By investing in basic science research and organizing our knowledge into an evolutionary framework, we will be better prepared to respond to the next emerging infectious disease.