Zoonotic spillover, which is the transmission of a pathogen from a vertebrate animal to a human, presents a global public health burden but is a poorly understood phenomenon. Zoonotic spillover requires several factors to align, including the ecological, epidemiological and behavioural determinants of pathogen exposure, and the within-human factors that affect susceptibility to infection. In this Opinion article, we propose a synthetic framework for animal-to-human transmission that integrates the relevant mechanisms. This framework reveals that all zoonotic pathogens must overcome a hierarchical series of barriers to cause spillover infections in humans. Understanding how these barriers are functionally and quantitatively linked, and how they interact in space and time, will substantially improve our ability to predict or prevent spillover events. This work provides a foundation for transdisciplinary investigation of spillover and synthetic theory on zoonotic transmission.