Abstract Most bats weigh less than 10 g. Megachiropterans are considerably heavier than microchiropterans, possibly because of their different ancestry or because they do not use laryngeal sonar. The predominance of medium-sized to small species of bats is compatible with general theories of extinction and speciation rates in relation to body size. There are few obvious links between diet and body size. It is more likely that biophysical factors associated with flight and/or echolocation constrain body size in bats. Models of flight power predict that flying vertebrates could weigh up to 12 kg, but the largest bat weighs under 1.5 kg. Bats radiated to fill the niche of nocturnal aerial insectivores, and echolocation is an effective way of detecting insects in the dark. However, high frequencies must be used to give strong echoes from small targets. Call frequency scales negatively with mass in five families of bats. Bats must probably be small to produce ultrasound. Because larger echolocating bats call at lower frequencies (hence long wavelengths), it has been proposed that they may not be able to detect small insects effectively. Large bats might therefore have a narrow dietary niche, and the need to rely on large, scarce prey would not favour the evolution of large size. However, large bats in fact seem to have broader dietary niche breadths than smaller species. Flapping and calling are coupled in echolocating bats as an energy-saving mechanism. Wingbeat frequency decreases as body size increases and aerial insectivorous bats generally emit one or fewer pulses per wingbeat. Aerial insectivorous bats may therefore be prevented from evolving large size because they would not be able to produce echolocation calls at a rate high enough to catch sufficient insects to meet the energetic demands associated with being large.