The rapid succession of the pandemic of arbovirus diseases, such as dengue, West Nile fever, chikungunya, and Zika fever, has intensified research on these and other arbovirus diseases worldwide. Investigating the unique mode of vector-borne transmission requires a clear understanding of the roles of vertebrates. One major obstacle to this understanding is the ambiguity of the arbovirus definition originally established by the World Health Organization. The paucity of pertinent information on arbovirus transmission at the time contributed to the notion that vertebrates played the role of reservoir in the arbovirus transmission cycle. Because this notion is a salient feature of the arbovirus definition, it is important to reexamine its validity. This review addresses controversial issues concerning vertebrate reservoirs and their role in arbovirus persistence in nature, examines the genesis of the problem from a historical perspective, discusses various unresolved issues from multiple points of view, assesses the present status of the notion in light of current knowledge, and provides options for a solution to resolve the issue.