When dinosaurs walked the Earth, flying reptiles called pterosaurs, ranging from the size of a sparrow to that of a two-seater plane, ruled the skies.

Sordes pilosus lived about 155 million years ago near a lake in what is now southern Kazakhstan where it likely dined on fish and other small prey. Its broad wings stretched from its wing bones to its ankles, and another flap of skin connected its legs, which it may have pumped during flight. Some fossils show that it kept warm with a thick coat of fibres similar to fur AMNH 2014

These winged reptiles – the first vertebrates to evolve powered flight – are the focus of Pterosaurs: Flight in the Age of Dinosaurs, an exhibition at the American Museum of Natural History in New York.

The show – featuring rare fossils and casts from Italy, Germany, China, United States, United Kingdom and Brazil as well as life-size models – focuses on how these reptiles gained their ability to fly.

When pterosaurs first appeared more than 220 million years ago, the earliest species were about the size of a modern seagull, but the group evolved into an array of species ranging from pint-size to truly gargantuan, including species that were the largest flying animals to have existed.

Pterosaur fossils are extremely scarce, and their closest living relatives — crocodiles and birds — are vastly different, so even the most elementary questions about how these extinct animals flew, fed, mated, and raised their young are still mysteries.

But recent discoveries have provided new clues to their behaviour. Like other flying animals, pterosaurs spent part of their lives on the ground. A fossil trackway from Utah reveals pterosaurs walked on four limbs and may have congregated in flocks. A cast of the first known fossil pterosaur egg, found in China in 2004, shows that pterosaur young were likely primed for flight soon after hatching.

Pterosaurs needed to generate lift just like birds and bats, but all three animal groups evolved the ability to fly independently, developing distinctly different wings.

A spectacular pterosaur fossil known as Dark Wing, on view for the first time outside Germany, features preserved wing membranes and reveals long fibres that extended from the front to the back of its wings to form a series of stabilising supports. These muscle fibres probably helped pterosaurs adjust the tension and shape of their wings.

Pterosaurs: Flight in the Age of Dinosaurs lands at the American Museum of Natural History in New York on Saturday 5 April and runs until 4 January 2015. Museum admission is free to all New York City school and camp groups.