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The following text is by David Maddison, from the Tree of Life page on Pterygota, and is reproduced here under teh Creative Commons license - MAK120516
Insects were the first organisms on Earth to evolve active flight. It is likely that the ability to fly arose only once in insects, over 300 million years ago in the Carboniferous period. About 70 million years later active flight arose within vertebrates (pterosaurs), followed by separate origins in birds and bats. Winged insects, or pterygotes, have radiated into over 100 times more species than all of the winged vertebrate lineages combined.
Many groups of insects have subsequently lost the ability to fly. Some of these (lice and fleas, for example) have lost all remnants of wings. It is only through their evident relationship with particular groups of winged insects (lice are closely related to psocids [book lice]; fleas are related to flies) that it is clear that their ancestors had wings.
Two groups of pterygotes evolved the ability to fold their wings back flat against their abdomens. The largest of these is the clade Neoptera ("new wing"). Remaining insects are sometimes referred to as Paleoptera ("old wing"), because they lack the sophisticated wing-folding mechanism of neopterous insects. Members of paleopterous insects cannot fold their wings back over their abdomens, with the exception of the extinct order Diaphanopterodea, which could fold their wings using a mechanism different than Neoptera. (Some neopterous insects, such as butterflies, can no longer fold their wings against their abdomen, but this clearly represents a secondary loss.)
David R. Maddison, ToL CC-BY 2002
Early Devonian to Recent
Phylogeny: Insecta : Archaeognatha + (Monura + (Thysanura + * : Rhyniognatha + (Ephemeroptera + Palaeodictyopteroida + Odonatoptera + Neoptera)))
Comments: veined wings on the second (meso-) and third (meta-) thoracic segment. - DRM02
Links Tree of Life, Encyclopedia of Life, Wikipedia; Fossil Insects by Roy J. Beckemeyer (focus on the Permian fossil insect Lagerstätten of Kansas and Oklahoma (The Wellington Formation sites) MAK120516