These cousins of the dinosaur are typically portrayed as cawing, gawky fliers with all the agility of a World War I biplane.
Now, though, computer scanning of fossilised pterosaur skulls has thrown up a radically different picture.
They reveal a creature whose highly specialised brain gave it extraordinary control over its wing surfaces, making it so nimble that it could probably outperform modern birds.
Researchers led by Lawrence Witmer of Ohio University carried out high-resolution X-ray computer tomography to build a 3D image of the skulls of two pterosaurs.
One was of Rhamphorhynchus, a long-tailed, crow-sized creature that lived between 163 and 144 million years ago.
The other was of Anhanguera, a large pterosaur with a short tail which lived during the Lower Cretaceous period, between 144 and 97.5 million years ago.
Compared to their mass, the brain that filled the skulls of these first vertebrate fliers would have been smaller than that of modern birds, Witmer's team say.
The likely reason for this is that birds descended from relatively big-brained theropod dinosaurs, whereas pterosaurs inherited their grey matter from smaller-brained reptiles known as archosaurs.
But the pterosaurs' big plus was to have outsized brain organs called the floccular lobes, which play a big role in processing sensory data and semi-circular canals, which are important in providing balance.
"Equipped with their 'smart' wings, pterosaurs would have excellent flight control... Despite their antiquity, they could even have outperformed modern birds and bats"
Berlin's Humboldt University
Witmer's team suggests that the pterosaurs' "enormous" lobes were used to process information sent back to the brain from sensors on from their wings.
Pterosaurs did not have feathers - they had a membrane of skin that stretched from their claw-like thumb and over its fingers.
Exciting recent finds of pterosaurs in Germany and China show that these membranes, far from being insensitive and leather-like, were remarkably complex, comprising a web of structural fibres, blood vessels and fine muscles.
So, by fine-controlling the shape of their wings, the creatures could exploit even the slightest breeze to make tight turns and swooping dives, all at a low cost in energy.
"Equipped with their 'smart' wings, pterosaurs would have excellent flight control," David Unwin, a paleontologist of the Museum of Natural Science at Berlin's Humboldt University, said in a commentary.
"Despite their antiquity, they could even have outperformed modern birds and bats."