Basically an essay for my personal project (as well as for JPL's "New Dinosaurs").
Out of all flying vertebrates that ever lived, pterosaurs are probably the most impressive ones. Specialized winged sauropsids, these produced the largest fliers ever, and produced an unique set of adaptations for life in the air. Their wings are composed of a complex membrane composed of not only skin, but also muscle and collagen fibers (used to make it stronger and keep its shape while flying), and that is supported by the arm and a very long fourth finger, that is attached to the body and extended along it until the ankles. In addition they also have a smaller membrane that attaches to the shoulder and runs across the arm (propatagium), which ends on an elongated wrist bone known as pteroyd, used in the same way as birds use their allula; another membrane runs along the legs (uropatagium). Pterosaurs have an air sac pulmonary system, pretty much like dinosaurs, very efficient for the high oxygen demands of their warm blooded metabolism. The advanced pterodactyloid pterosaurs have also other adaptations for flight, such as a nasoanteorbital frenestra (a fusion of the nostril with the anteorbital frenestra, a "hole" in the skull of archosaurs between the nostril and the orbit), a notarium (a fusion of dorsal vertebrae, used to stabilize the body during flight), long metacarpals (so that the weight of the wing membrane doesn't fall all on the wing finger; it also aids on terrestrial locomotion) and short tail; more advanced species also lack teeth. Pterosaurs reproduce via egg laying, burrying their eggs on the ground. While some species might show parental care, the "flaplings" are nonetheless precocial, being able to fly since they are born, and because they already start looking for food they occupy several niches across their lifetime (which means a smaller species diversity compared to birds)
Pterosaurs first appeared in the Triassic, as long tailed primitive forms such as Eudimorphodon. They seem to have had evolved from basal ornithodirans like Lagosuchus, which also gave rise to dinosaurs. Soon they dominated the air, and these basal forms became very diverse until the end of the Jurassic, when the first pterodactyloids evolved; indeed, only anurognathids seemed to had survived. Pterodactyloids soon diversified, producing a larger amount of species taking over a lot more niches. Then, towards the middle Cretaceous, they seemed to that been declining, as only the larger genera appear in the fossil record; however, smaller ones did had survived, only that they were sheldomly preserved in the fossil record (at least until the Eocene, when they reappear in laggerstaten fossil sites like Messel, absent from the late Cretaceous). As the Cenezoic came, they preserved a middle diversity; the Paleocene/Eocene Thermal Maximum exterminated the pelagic pteranodonts, while the later Pliocene cooling caused extinctions in Europe and (to a lesser extent) in North America. Nonetheless, pterosaurs are still common and recolonised the regions they had disappeared from in the interglacial periods.
The most basal living pterosaurs, and a somewhat poorly understood linage. Mainly nocturnal fliers, they avoid competion with pterodactyloids, and took a nightjar like lifestyle, feeding on moths and other night flying insects. Relying on vision to guide themselves, they share their environment with volaticothere mammals (bat analogues), which use sonar to find their way in the dark; anurognathids also have often bristles to sense the vibrations of flying insects, and down on their wing membranes in order to decrease the sound created by the wing flapping. Anurognathids are for all purposes Caprimulgiforme analogues, having a broad, short snout like insectivore birds have short and broad bills (making their heads somewhat frog like); they also have bigger uropatagia than pterodactyloids, supported by a very long first toe, acting like a the forked tail of insectivore birds. While there's not a lot of species diversity (35+) the ones present are quite common.
The typical anurognathoids, nocturnal animals with short and broad wings that live in forests. Barely changed since the Mesozoic, they are mostly aerial insectivores, but some became vertebrate predators like our world's frogmouths, and a particular species, the Cliff Ghast (Daemonognathus phillippullmani) became a large diurnal scavenger/predator from Eurasian mountain ranges, competing with predatory birds.
Although the earliest members of this clade seem to have first appeared in the Eocene, genetic data indicates a much older origin, probably dating from the Cretaceous or even earlier (though its unlikely modern looking species evolved prior to the Paleocene/Eocene periods. Unlike their more conservative relatives, they are diurnal, and so they lost adaptations like the down covered wing membranes and bristles, and have longer and thinner wings. As a whole, they resemble pterosaurian swallows (ence their english name, "swallow lizards"), and that even reflects itself where they lay their eggs; rather than burrying them, they actually build nests not too different from those of our world's swallows, keeping inaccessible to ground dweeling predators. There are more or less 13 species of these fliers divided in two genera, Hirundosaurus and Ranorhynchus, the first more common in Eurasia, Africa and the Americas while the other being restricted to Ocenia and Pacific islands (and yet with a larger species count).
The rest of the living pterosaurs belong to this clade, which has developed several adaptations absent in more basal pterosaurs as mentioned in the first paragraph of this essay.
A basal linage of pterodactyloids which included the famous Pterodactylus, they are notorious for their wading habits, having evolved large webbed feet for that purpose. Although they produced stork and heron like forms in the past, they all modern species (and most extinct ones) are filter feeders, using very thin and numerous teeth to trap small animals in their beaks. Smaller forms managed to survive in the Cretaceous, barely becoming preserved, and they only reappered significantly in the Eocene, when laggerstaten fossil sites also reappeared. Relatively more common in the northern hemisphere, they suffered a heavy blow when the ice ages came. Now days, a few species still exist, forming large flocks in wetland areas like flamingoes.
Having declined since the Cretaceous, they are now reduced to a two cryptic species, the african Kongamato (Amphipterus africanus) and the Ropen (Lucipterosaurus aumalae). Both are aerial predators from rainforest and wetland areas, preying on small tetrapods and fish. They seem to be both solitary; the Kongamato is highly territorial and agressive, often attacking large animals that happen to be on their nesting sites. Little is known about the Ropen; it seems to be nocturnal, and its wing membranes glow due to a symbiotic relationship with a special specie of fungus.
Probably the most diverse linage of modern pterosaurs aside from anurognathids. Represented as the huge azhdarchids during the late Cretaceous, the globalization of rainforests drove the large species to polar areas or coastoal zones, since they couldn't live in the dense forests. The end result was that these pterosaurs diverged into three separate clades:
Relatively conservative forms, they are hardly different from their Cretaceous relatives. They are divided into five species and their range pretty much covers all of the large landmasses.
During the Eocene, a linage of azhdarchids decreased drastically in size via neoteny (since pterosaurs are highly precocial and occupy many niches across their lifetime, it would be fairly easy for them to start reproducing at an earlier stage of their lives and not needing to grow besides that phase anymore). Having specialized to a life in rainforests, these relatively small pterosaurs occupy niches occupied in our world by hornbills and toucans; this situation is rather the inverse than in our world's hornbills, as while grassland dweeling pterosaurs produced rainforest forms while rainforest dweeling hornbills produced savanna dweeling forms.
Also in the Eocene, a linage of azhdarchids became isolated in Africa (then an island) and lost their ability to fly. Their wing membranes were lost (aside from a small membrane supported by a very reduced wing finger), and the usually plantigrade pterosaurian hind feet became digitigrade, just like the front ones (though not to that extreme). Their front feet (in a lateral position in most pterosaurs) also rotated forward, and their bodies became more robust. Being omnivores with carnivore tendencies, they took over the niches of oviraptors in Eurasia after the colision of Africa with that continent. In the americas, though, non-avimimid oviraptors (since avimimids took over small ornithopod niches) still remained somewhat dominant, specially after the interchange with South America that occured in the Pliocene. Apterocheirids are quite bizarre in the way how they reproduce; because pterosaurs lay eggs with very thin shells, ovivipary managed to evolve in these flightless forms, something that birds can't evolve due to their hard shelled eggs. Juveniles are protected by the parents, but more basal forms (most insular) don't display it; instead, the juveniles take an arboreal lifestyle, using wing membranes to glide (they later disappear aside from the vestigial structure, mentioned before)
[I'll give specie examples later]