Bat wing morphology is considered in relation to flight performance and flight behaviour to clarify the functional basis for eco-morphological correlations in flying animals. Bivariate correlations are presented between wing dimensions and body mass for a range of bat families and feeding classes, and principal-components analysis is used to measure overall size, wing size and wing shape. The principal components representing wing size and wing shape (as opposed to overall size) are interpreted as being equivalent to wing loading and to aspect ratio. Relative length and area of the hand-wing or wingtip are determined independently of wing size, and are used to derive a wingtip shape index, which measures the degree of roundedness or pointedness of the wingtip. The optimal wing form for bats adapted for different modes of flight is predicted by means of mechanical and aerodynamic models. We identify and model aspects of performance likely to influence flight adaptation significantly; these include selective pressures for economic forward flight (low energy per unit time or per unit distance (equal to cost of transport)), for flight at high or low speeds, for hovering, and for turning. Turning performance is measured by two quantities: manoeuvrability, referring to the minimum space required for a turn at a given speed; and agility, relating to the rate at which a turn can be initiated. High flight speed correlates with high wing loading, good manoeuvrability is favoured by low wing loading, and turning agility should be associated with fast flight and with high wing loading. Other factors influencing wing adaptations, such as migration, flying with a foetus or young or carrying loads in flight (all of which favour large wing area), flight in cluttered environments (short wings) and modes of landing, are identified. The mechanical predictions are cast into a size-independent principal-components form, and are related to the morphology and the observed flight behaviour of different species and families of bats. In this way we provide a broadly based functional interpretation of the selective forces that influence wing morphology in bats. Measured flight speeds in bats permit testing of these predictions. Comparison of open-field free-flight speeds with morphology confirms that speed correlates with mass, wing loading and wingtip proportions as expected; there is no direct relation between speed and aspect ratio. Some adaptive trends in bat wing morphology are clear from this analysis. Insectivores hunt in a range of different ways, which are reflected in their morphology. Bats hawking high-flying insects have small, pointed wings which give good agility, high flight speeds and low cost of transport. Bats hunting for insects among vegetation, and perhaps gleaning, have very short and rounded wingtips, and often relatively short, broad wings, giving good manoeuvrability at low flight speeds. Many insectivorous species forage by `flycatching' (perching while seeking prey) and have somewhat similar morphology to gleaners. Insectivorous species foraging in more open habitats usually have slightly longer wings, and hence lower cost of transport. Piscivores forage over open stretches of water, and have very long wings giving low flight power and cost of transport, and unusually long, rounded tips for control and stability in flight. Carnivores must carry heavy loads, and thus have relatively large wing areas; their foraging strategies consist of perching, hunting and gleaning, and wing structure is similar to that of insectivorous species with similar behaviour. Perching and hovering nectarivores both have a relatively small wing area: this surprising result may result from environmental pressure for a short wingspan or from the advantage of high speed during commuting flights; the large wingtips of these bats are valuable for lift generation in slow flight. The relation between flight morphology (as an indicator of flight behaviour) and echolocation is considered. It is demonstrated that adaptive trends in wing adaptations are predictably and closely paralleled by echolocation call structure, owing to the joint constraints of flying and locating food in different ways. Pressures on flight morphology depend also on size, with most aspects of performance favouring smaller animals. Power rises rapidly as mass increases; in smaller bats the available energy margin is greater than in larger species, and they may have a more generalized repertoire of flight behaviour. Trophic pressures related to feeding strategy and behaviour are also important, and may restrict the size ranges of different feeding classes: insectivores and primary nectarivores must be relatively small, carnivores and frugivores somewhat larger. The relation of these results to bat community ecology is considered, as our predictions may be tested through comparisons between comparable, sympatric species. Our mechanical predictions apply to all bats and to all kinds of bat communities, but other factors (for example echolocation) may also contribute to specialization in feeding or behaviour, and species separation may not be determined solely by wing morphology or flight behaviour. None the less, we believe that our approach, of identifying functional correlates of bat flight behaviour and identifying these with morphological adaptations, clarifies the eco-morphological relationships of bats.