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Over the evolutionary continuum, animals have faced similar fundamental challenges of acquiring molecular oxygen for aerobic metabolism. Under limitations and constraints imposed by factors such as phylogeny, behaviour, body size and environment, they have responded differently in founding optimal respiratory structures. A quintessence of the aphorism that “necessity is the mother of invention”, gas exchangers have been inaugurated through stiff cost-benefit analyses that have evoked transaction of trade-offs and compromises. Cogent structural-functional correlations occur in constructions of gas exchangers within and between taxa, morphological complexity and respiratory efficiency increase with metabolic capacities and oxygen needs. Highly active, small endotherms have relatively better-refined gas exchangers compared with large, inactive ectotherms. Respiratory structures have developed from the plain cell membrane of the primeval prokaryotic unicells to complex multifunctional ones of the modern Metazoa. Regarding the respiratory medium used to extract oxygen from, animal life has had only two choices – water or air – within the biological range of temperature and pressure the only naturally occurring respirable fluids. In rarer cases, certain animals have adapted to using both media. Gills (evaginated gas exchangers) are the primordial respiratory organs: they are the archetypal water breathing organs. Lungs (invaginated gas exchangers) are the model air breathing organs. Bimodal (transitional) breathers occupy the water-air interface. Presentation and exposure of external (water/air) and internal (haemolymph/blood) respiratory media, features determined by geometric arrangement of the conduits, are important features for gas exchange efficiency: counter-current, cross-current, uniform pool and infinite pool designs have variably developed.