Pneumatic (air-filled) postcranial bones are unique to birds among extant tetrapods. Unambiguous skeletal correlates of postcranial pneumaticity first appeared in the Late Triassic (approximately 210 million years ago), when they evolved independently in several groups of bird-line archosaurs (ornithodirans). These include the theropod dinosaurs (of which birds are extant representatives), the pterosaurs, and sauropodomorph dinosaurs. Postulated functions of skeletal pneumatisation include weight reduction in large-bodied or flying taxa, and density reduction resulting in energetic savings during foraging and locomotion. However, the influence of these hypotheses on the early evolution of pneumaticity has not been studied in detail previously. We review recent work on the significance of pneumaticity for understanding the biology of extinct ornithodirans, and present detailed new data on the proportion of the skeleton that was pneumatised in 131 non-avian theropods and Archaeopteryx. This includes all taxa known from significant postcranial remains. Pneumaticity of the cervical and anterior dorsal vertebrae occurred early in theropod evolution. This 'common pattern' was conserved on the line leading to birds, and is likely present in Archaeopteryx. Increases in skeletal pneumaticity occurred independently in as many as 12 lineages, highlighting a remarkably high number of parallel acquisitions of a bird-like feature among non-avian theropods. Using a quantitative comparative framework, we show that evolutionary increases in skeletal pneumaticity are significantly concentrated in lineages with large body size, suggesting that mass reduction in response to gravitational constraints at large body sizes influenced the early evolution of pneumaticity. However, the body size threshold for extensive pneumatisation is lower in theropod lineages more closely related to birds (maniraptorans). Thus, relaxation of the relationship between body size and pneumatisation preceded the origin of birds and cannot be explained as an adaptation for flight. We hypothesise that skeletal density modulation in small, non-volant, maniraptorans resulted in energetic savings as part of a multi-system response to increased metabolic demands. Acquisition of extensive postcranial pneumaticity in small-bodied maniraptorans may indicate avian-like high-performance endothermy.