The intimate relationship between virus and host cell can result in highly adapted viruses that are restricted to a single host. However, some viruses have the ability to infect multiple host species. Remarkably, hepatitis E viruses (HEV) comprise genotypes that are either ‘single-host’ or ‘multi-host’ genotypes, a trait that raises fundamental questions: Why do different genotypes differ in their host range, despite a high degree of genomic similarity? What are the underlying molecular determinants that shape species barriers? Here, we review the current knowledge of viral and host determinants that may affect the evolutionary trajectories of HEV. We also provide a perspective on techniques and methods that address open questions of HEV host range and adaptation.