Bats are known to harbor and transmit many emerging and re-emerging viruses, many of which are extremely pathogenic in humans but do not cause overt pathology in their bat reservoir hosts: henipaviruses (Nipah and Hendra), filoviruses (Ebola and Marburg), and coronaviruses (SARS-CoV and MERS-CoV). Direct transmission cycles are often implicated in these outbreaks, with virus shed in bat feces, urine, and saliva. An additional mode of virus transmission between bats and humans requiring further exploration is the spread of disease via arthropod vectors. Despite the shared ecological niches that bats fill with many hematophagous arthropods (e.g., mosquitoes, ticks, biting midges, etc.) known to play a role in the transmission of medically important arboviruses, knowledge surrounding the potential for bats to act as reservoirs for arboviruses is limited. To this end, a comprehensive literature review was undertaken examining the current understanding and potential for bats to act as reservoirs for viruses transmitted by blood-feeding arthropods. Serosurveillance and viral isolation from either free-ranging or captive bats are described in relation to four arboviral groups (Bunyavirales, Flaviviridae, Reoviridae, Togaviridae). Further, ecological associations between bats and hematophagous viral vectors are characterized (e.g., bat bloodmeals in mosquitoes, ingestion of mosquitoes by bats, etc). Lastly, knowledge gaps related to hematophagous ectoparasites (bat bugs and bed bugs (Cimicidae) and bat flies (Nycteribiidae and Streblidae)), in addition to future directions for characterization of bat-vector-virus relationships are described.