Many aspects of animal behaviour are affected by real-time changes in the risk of predation. This conclusion holds for virtually all taxa and ecological systems studied, but does it hold for bats? Bats are poorly represented in the literature on anti-predator behaviour, which may reflect a lack of nocturnal predators specialized on bats. If bats actually experience a world with minimal anti-predator concerns, then they will provide a unique contrast within the realm of vertebrate ecology. Alternatively, such predator-driven behaviour in bats may not yet be fully understood, given the difficulties in working with these highly mobile and nocturnal animals. We provide a wide-ranging exploration of these issues in bat behaviour. We first cover the basic predator-prey information available on bats, both on potential predators and the ways in which bats might perceive predators and respond to attacks. We then cover work relevant to key aspects of bat behaviour, such as choice of daytime roosts, the nature of sleep and torpor, evening roost departures, moonlight avoidance, landscape-related movement patterns, and habitat selection. Overall, the evidence in favour of a strong influence of predators on bat behaviour is equivocal, with the picture clouded by contradictory results and a lack of information on potential predators and the perception of risk by bats. It seems clear that day-active bats run a considerable risk of being killed by diurnal raptors, which are able to capture bats with relative ease. Thus, bats taking advantage of a pulse of insects just prior to sunset are likely taking risks to gain much-needed energy. Further, the choice of daytime roosts by bats is probably strongly influenced by roost safety. Few studies, however, have directly addressed either of these topics. As a group, insectivorous temperate-zone bats show no clear tendency to avoid apparently risky situations, such as activity on moonlit nights. However, some observations are consistent with the idea that predation risk affects choice of movement paths and feeding areas by temperate-zone bats, as well as the timing of roost departures. The behaviour of tropical bats, on the other hand, seems more generally influenced by predators; this is especially true for tropical nectarivores and frugivores, but also for insectivorous bats. Presumably there are more serious predators on bats in the tropics (e.g. specialized raptors or carnivorous bats), but the identity of these predators is unclear. More information is needed to assess fully the influence of predators on bat behaviour. There is much need for work on the ways in which bats perceive predators via auditory, visual, and olfactory cues, and whether bats have some knowledge of the risks posed by different predators. Also needed is information on how predators attack bats and how bats react to attacking predators. Difficult to obtain, but of critical value, will be information on the nature of the predation risk experienced by bats while away from roosts and during the full darkness of night.