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 furAMNH 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.

Pterosaurs evolved from an ancestor that may have resembled Scleromochlus taylori, a terrestrial reptile that lived around 230 million years ago. Scleromochlus probably ran or leaped around on its long hind legs. Based on some of the bones in its foot, scientists think it was an early relative of both pterosaurs and dinosaursAMNH 2014
Preondactylus buffarinii
One of the oldest known pterosaurs, Preondactylus buffarinii lived around 220 million years ago near an inland sea in what is now northern Italy. Like many early pterosaurs, it had relatively short wings (wingspan of 18 inches), long legs and a very long tailAMNH 2014
Wukongopterus fossil cast: This recently discovered pterosaur, found in Liaoning Province, China, has a long, straight tail, like most primitive species on the pterosaur evolutionary tree. But it also had some advanced traits, such as relatively long neck vertebrae. Scientists think this pterosaur could be a transitional species, evolving as pterosaur body types started to changeAMNH/C. Chesek

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.

fossil of Nemicolopterus crypticus
This cast of a fossil of Nemicolopterus crypticus, one of the smallest pterosaurs, was discovered in northeastern China in 2008. Its fossil skeleton, with its curved toe bones, suggests it could cling to the branches or trunks of trees. Nemicolopterus, about the size of a modern sparrow, may have darted through forests hunting for insects, snapping them up in its toothless jawsAMNH/C. Chesek
This large pterosaur species, Quetzalcoatlus northropi, lived around 70 million years ago on a plain in what is now western Texas. With a wingspan of at least 33 feet, it was about as big as a two-seater plane – larger than any other known flying animal. It was named after Quetzalcoatl, a Mexican god of the airAMNH 2014
This humerus, or upper arm bone, belonged to Quetzalcoatlus northropi, one of the largest pterosaurs found to date. A geology student discovered this fossil in a gulch in southwestern Texas, but the only remains he could find were parts of one wing. The massive knob at the shoulder end was an attachment point for powerful muscles – a clue that this animal was capable of flightAMNH/C. Chesek
Quetzalcoatlus northropi model
Museum staff work on a full-size model of Quetzalcoatlus northropi, one of the largest pterosaurs, with a wingspan of at least 33 feetAMNH/R. Mickens

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.

This sandstone slab from Utah is a relic from more than 140 million years ago, when pterosaurs strolled on tidal flats near a sea in what is now the American West. The nine sets of prints are of different sizes, so they may have been left by more than one species, or by a group that included both young and adults. Today, these fossil tracks help reveal how the pterosaurs moved: not like birds but like bats, walking on all four limbsAMNH/C. Chesek
This cast of a pterosaur egg shows a fossilised pterosaur curled up, with its wings wrapped around its body. The skeleton is nearly complete, indicating that the young pterosaur was almost ready to come out of its shell. Its wing bones are long and fairly solid, so it would probably have been able to fly soon after hatchingAMNH/C. Chesek

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.

dark wing
In this remarkable Rhamphorhynchus muensteri fossil, discovered in Germany in 2001, the wing tissues are so well preserved that scientists have been able to see fine details in their structure. Under ultraviolet light, researchers detected layers of skin threaded with blood vessels, muscles and long fibres that stiffened the wing. Because of the shadowy colour of the wing membrane, palaeontologists call this fossil Dark WingAMNH/D. Finnin
Rhamphorhynchus muensteri is a dagger-toothed pterosaur from the Late Jurassic (about 150 million years ago). It had a long tail, with a stiff flap of skin called a vane at the end that stabilised flight. Some scientists think this membrane faced sideways, like a fish tail, and helped prevent rocking from side to side. Others think it lay flat, like a paddle, and helped the flying pterosaur control its elevationAMNH 2014

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.

Thalassodromeus sethi had a crest three times larger than the rest of its skull, when seen from the side. Indeed, it had the largest crest of any known vertebrate. This large pterosaur species, with a wingspan of 14 feet, lived around 110 million years ago near a lagoon in what is now BrazilAMNH 2014
Thalassodromeus skull
The huge, flat crest of Thalassodromeus sethi contained a network of branching channels. These visible grooves suggest that during life, a network of blood vessels covered the crest below the skin. These channels might have sent warm blood to the crest's surface, cooling the animal as it flewAMNH/C. Chesek