Bats belong to the order Chiroptera that represents the second largest order of mammals with more than 1200 species and an almost global distribution. Environmental changes and deforestation have severely influenced many ecosystems, intensifying the contact between wildlife and humans. In recent years, bats have been found to harbor a number of different viruses with zoonotic potential, as well as a great diversity of astroviruses, for which the question of zoonotic potential remains unanswered to date. Human astroviruses have been identified as the causative agent for diarrhea in children and immunocompromised patients. For a long time, astroviruses have been considered to be strictly species-specific. However, a great genetic diversity has recently been discovered among animal and human astroviruses that might indicate the potential of these viruses to cross species barriers. Furthermore, our knowledge about the tissue tropism of astroviruses has been expanded to some neurotropic strains that have recently been shown to be responsible for encephalitis in humans and livestock. This review gives an overview on what is known about astroviruses in bats, humans and livestock, especially bovines and pigs. Future research activities are suggested to unravel astrovirus infection dynamics in bat populations to further assess the zoonotic potential of these viruses.