When searching for the biggest beast ever to take to the sky, you might think it sensible to look at the biggest birds alive today.

One modern-day giant weighs up to 330lb (150kg) and can stand 9ft (2.75m) tall with wings spanning almost 6.5ft (2m). But this is the ostrich, which famously does not fly.

Neither do any of the rest of the big birds in the ratite family, which includes the emu, rhea and cassowary. Similarly, the 3ft (1m) emperor penguin and marginally shorter king penguin both reach impressive weights but only "fly" underwater.

Arguably the heaviest flying bird is the kori bustard of southern Africa. Males can reach 42lb (19kg) with wingspans of up to 2.5ft (75cm), but these ground-dwelling birds rarely fly.

Concentrating on birds that are in their element on the wing, the Andean condor is often named as the largest flying bird. Among these mountain-dwelling South American vultures, males can tip the scales at up to 33lb (15kg) and have wings that can span 10ft 5in (3.2m).

Above the high seas, there is a bird who might only weigh around 19lb (8.5kg) but its wings routinely span more than 9ft 10in (3m). The wandering albatross holds the longest wingspan record for any flying bird, the maximum having been recorded at 11ft 10in (3.63m).

It can fly without any mechanical cost thanks to "dynamic soaring": it uses wind energy to cover thousands of miles without the effort of flapping.

Of course, birds are not the only animals with impressive wings. Known variously as megabats, flying foxes or fruit bats, a number of tropical bats have also grown large.

"[Acerodon jubatus] is largest by weight, weighing in at just over a kilogram," says Tammy Mildenstein of the Southeast Asian Bat Conservation Research Unit, who has worked extensively with bats in Indonesia. "There are a couple of Pteropus species, Pteropus vampyrus and Pteropus giganteus, that are slightly larger by wingspan. All are very close in weight and have nearly 2m [6.5ft] wingspans."

While one of those Latin names suggests something more sinister, the bats actually maintain their size on a diet of fruit. Some also drink nectar and eat leaves. They forage in the forest canopy because their wings are too large for them to easily navigate between the trees.

"The advantage of having large kite-like wings is they can glide and fly very long distances," says Mildenstein. "This helps flying foxes travel the average 50km [30 miles] through forests each night to collect food."

Flight is useful for any animals that need to travel long distances for food or mates. But to find true giants we need to step back through time to an era before the continents had settled into their current positions.

The largest birds lived around 25 million years ago, according to fossil evidence.

"Pelagornis sandersi is the largest flying bird on record by wingspan," explains Michael Habib of the University of Southern California in Los Angeles, an expert in ancient flying animals.

This "seagull on steroids" had wings that could measure 7.38m (24ft 2in) from tip to tip and is estimated to have weighed between 20 and 40kg (44-88lb).

In contrast, the heaviest known flying bird, Argentavis, was more than twice this weight but had a shorter wingspan. Remains in the La Brea Tar Pits of Los Angeles suggest it lived more recently, around 6 million years ago, according to Habib.

Jumping even further back in time, we leave the recognisable birds and meet the pterosaurs.

These reptiles evolved the power of flight before birds, and a few did so on a grand scale. Named after the Mesoamerican feathered serpent god, Quetzalcoatlus northropi lived around 68 million years ago and flew on wings spanning 34ft (10.4m).

Habib says there are a few related azhdarchid pterosaurs that tie for the title of biggest flying beast.

"Wingspan estimates are typically pretty reliable," he says. "Mass estimates are much less reliable except for the few species where we have complete, uncrushed skeletons."

"That said, most mass estimates for the largest pterosaurs do converge, using multiple methods, around a 200-260kg [440-570lb] range at present, which represents decent confidence."

In other words, they weighed as much as an upright piano and their wings were longer than a London bus.

Colin Palmer at the University of Bristol, UK, has worked with Habib to explore the mechanical limits of these giant pterosaurs. He estimates their maximum wingspan to be 36ft (11m), based on aerodynamic theory and the fossil record.

He says the fossil record for the largest species is patchy, but there is good evidence from scaling up the 23ft (7m) wingspans of related animals that fossilised more often.

"Calculations suggest the largest pterosaurs couldn't flap continuously," Palmer says. Instead, the estimated muscle mass of Quetzalcoatlus and its ilk suggests they had a similar flying style to modern condors.

"Large flyers typically can't sustain flapping for long periods," says Habib. "They are usually soaring animals, which means that they use powered flight part of the time and then unpowered flight the rest, using thermals, wind gradients, and other energy sources to stay aloft for long periods of time."

Taking off and landing also becomes an issue for really big animals.

Many modern birds use their legs to power their take-off and control their landing. You can see this at a bird table.

But once they are airborne, their legs are just extra weight to carry while the wings do the hard work. Species that fly long distances need lots of power in their chest muscles, and cannot afford excess baggage like big legs. Palmer says this explains the noisy, wing-beating take-offs and ungainly landings of swans.

In contrast, pterosaurs are thought to have used the same muscles for take-off and flying, pushing themselves off the ground with their forelimbs. They had air-filled bones, like modern birds, which kept their overall weight down.

The soft tissue wings of pterosaurs have rarely been preserved, but Palmer has used engineering knowledge to model the possibilities. Instead of feathers, pterosaur wings are thought to have been membranes, similar to bats'.

These wings stretched from one elongated digit to their ankle with reinforcing fibrous edges to help them fly efficiently. Palmer suggests these adaptations could be what allowed them to grow to such large sizes and become the dominant predators of their day.

But the golden age of flying giants is not necessarily behind us.

"In a few million years another group of birds may reach giant proportions; there's no way to know," says Habib.

"Bats can also get much larger than they do, mechanically, but the current range of ecologies and life histories among bats doesn't select for large size. There could easily be albatross-sized bats, if it were just a matter of mechanics."