So let's look at the timing of the pterosaurs' disappearance and the appearance of modern birds.
What better way to start than with this:
Here is the current evolution opinion:
"It is often thought that competition with early bird species may have resulted in the extinction of many of the pterosaurs. By the end of the Cretaceous, only large species of pterosaurs are known. The smaller species seem to have become extinct, their niche filled by birds,; however, pterosaur decline (if actually present) seems unrelated to bird diversity . At the end of the Cretaceous period, the great extinction which wiped out all non-avian dinosaurs and most avian dinosaurs as well, and many other animals, seemed to also take the pterosaurs. Alternatively, most pterosaurs may have been specialised for an ocean-going lifestyle. Consequently, when the K-T mass-extinction severely affected marine life that most pterosaurs fed on, they went extinct. However, forms like azhdarchids and istiodactylids weren't marine in habits."
"...and describe the gradual decline of pterosaurs at the same time modern birds radiate."
"It is clear that modern birds from at least the latest Cretaceous lived at the same time as archaic birds including Hesperornis, Ichthyornis, and the diverse Enantiornithiformes. Pterosaurs, which also coexisted with early crown [modern] birds, show notable changes through the Late Cretaceous. There was a decrease in taxonomic diversity, and small- to medium-sized species disappeared well before the end of the Cretaceous. A simple reading of the fossil record might suggest competitive interactions with birds, but much more needs to be understood about pterosaur life histories."