The use of available morphological characters in the interpretation of the flight of insects known only as fossils is reviewed, and the principles are then applied to elucidating the flight performance and techniques of Palaeozoic palaeopterous insects. Wing-loadings and pterothorax mass/total mass ratios are estimated and aspect ratios and shape-descriptors are derived for a selection of species, and the functional significance of wing characters discussed. Carboniferous and Permian ephemeropteroids ('mayflies') show major differences from modern forms in morphology and presumed flight ability, whereas Palaeozoic odonatoids ('dragonflies') show early adaptation to aerial predation on a wide size-range of prey, closely paralleling modern dragonflies and damselflies in shape and wing design but lacking some performance-related structural refinements. The extensive adaptive radiation in form and flight technique in the haustellate orders Palaeodictyoptera, Megasecoptera, Diaphanopterodea and Permothemistida is examined and discussed in the context of Palaeozoic ecology.