At approximately three o’clock in the afternoon of March 18, 1906, a strange craft rolled out onto a field near Paris. Looking like a large-wheeled shopping cart that had gotten entangled with a clothesline, the vehicle was escorted by its builder, a native of Romania named Trajan Vuia.

Bizarre-looking flying machines were not so unusual in those days; at the very dawn of the Age of the Airplane, no one really knew what a good design should look like, and Paris was the world hub of wild experimentation. But what Vuia was about to attempt was not merely to take to the air; no, he aimed for something grander: to take to the air in the world’s first flying car.

For five minutes, Vuia let the engine thrum. Then he settled into the wicker seat, grasped the steering wheel, and eased the throttle open. The winged buggy lurched forward, bouncing over the grassy ground as it gained speed. And then, after traveling about 150 feet, the craft lifted into the air. Climbing tremulously, it reached a dizzying height of three feet, then settled back down to touch the earth. Total distance traveled: about a dozen yards.

Even by the modest standards of the day, it was not a very impressive flight. But Vuia had scored the first success in a campaign that would ultimately outlive the young century, one which remains vital today. Indeed, were Vuia alive in 2012, he would undoubtedly be surprised that flying cars—legally road-worthy vehicles that can take off and soar through the air—remain commercially nonexistent, despite the best efforts of a never-ending stream of inventors, from backyard tinkerers to some of Detroit’s mightiest automakers. The dream remains much as it was in Vuia’s time: an intriguing notion which, apart from a few brief hops here and there, has refused to take flight. But will that always be the case? Is it possible that cutting-edge technology will transform this dusty vision into a vibrant reality? Could it be, in fact, that the supervehicle of our dreams is just around the corner?

The next major attempt came a dozen years later, when aviation pioneer Glenn Curtiss patented a vehicle he called the Autoplane. By then, the world of transportation had changed radically. Military innovations of World War I had transformed both airplanes and automobiles from curiosities to proven technologies. So the time should have been ripe for their hybrid to take hold. And indeed, compared with Vuia’s primitive contraption, Curtiss’s machine looked mechanically sophisticated. (If not particularly sleek; in surviving photos it resembles a Ford Model T that has backed into a Wright Flyer.) Curtiss received a patent for his contraption in 1919, but the machine was ever able to manage only short hops.

Curtiss fell afoul of the fundamental problem that would plague flying-car pioneers over the decades to come. “A car needs to be small so that the wind doesn’t flip it over, and it needs to be heavy so that if it runs into something, the driver has some chance of coming out in one piece,” explains Austin Meyer, an aeronautical-modeling software designer. “Airplanes are just the reverse. To fly efficiently they need to be as light as possible and have nice big long wings. You can’t have something that’s both heavy and light, and big and small, at the same time.”

Flying-car designers must contend with other design dilemmas, as well. Because a mechanical failure can be deadly, aircraft engines are usually connected directly to the propeller shaft for maximum reliability. Car engines, on the other hand, are connected to the wheels via gears, so that they can operate at a wide range of speeds. An airplane’s main wheels need to be near the center of gravity, so that the aircraft can rotate on landing and takeoff; a car’s wheels need to be as far from the center of gravity as possible, for stability in turns. And the list goes on. None of these problems are impossible to solve in themselves, but they force a would-be flying-car designer to make countless compromises. Inevitably, what results is a vehicle that is both car and plane—but not very good at being either one.

Still, in the years after Curtiss’s flop, the challenge remained catnip to a certain breed of challenge-loving inventor, especially in the aftermath of World War II, when a spate of returning pilots fueled a mania for recreational aviation.In the 1940s and ’50s, a pilot and adventurer named Robert Edison Fulton Jr. built a series of machines he called the Airphibian, which mated the wings and tail of a conventional light aircraft with the body of a buglike car; it could be detached and driven away at the end of each flight. The Fulton Airphibian was the first true flying car in one important sense: It was the first road-able aircraft certified as an airplane, and so it could legally both fly and drive.

In the process of testing the Airphibian, Fulton and his colleagues drove it for thousands of miles. In 1952, Popular Science sent a writer for a test-drive. He came away impressed—“The Airphibian was stable in the air,” he wrote. “It felt good”—and reported that it would go on sale to the public the following year. But with a top speed of just 60 mph on the ground and 110 mph in the air, the Airphibian proved a commercial disaster. In 1953 Fulton’s investors pulled the plug. Today, one of the few surviving examples is on display at the Smithsonian’s Udvar-Hazy Center near Washington, D.C.

Fulton’s vision did not die with his failure. Among those inspired by his efforts was a Washington state inventor named Moulton Taylor. Having met Fulton by chance during a business trip, Taylor immediately grasped a shortcoming of the other man’s approach: The car portion was effectively tethered to the airport, where the wings and tail were left behind. If a flying car could somehow drive away from the airstrip with its wings and tail attached, a pilot could fly out of a different airport than the one he flew into.

Taylor’s solution was a flying car that looked a good deal like Fulton’s, but which had foldable wings that could be pulled behind the car like a trailer. During the ’50s Taylor built six vehicles in three versions. He toured the country displaying them at automobile shows, but like Fulton he was never able to secure enough orders to begin production. He died in 1995, but one of his prototypes continues to fly to this day.

The ’50s and early ’60s were the true heyday of the flying car. Not only numerous small inventors, but also major corporations like Ford and Chrysler, dipped their toes into the waters. But none found a way to make the idea work. And as the ’60s gave way to the ’70s, the idea of tootling around the country in a half-car, half-airplane began to seem like a somewhat archaic brand of futurism. What the world really needed was something a bit more science-fictiony: a car that could leap into the air on a whim. And that’s just what Canadian engineer Paul Moller devised.

In 1991 Moller, a onetime professor of aeronautics at the University of California at Davis, unveiled a shiny red Batmobile-looking machine he called the M400 Skycar. With a T-tail, a bubble canopy, and four podlike fan units protruding from the side, it looked like it had been teleported from the distant future. Moller claimed that when perfected, his craft would be able to carry four people at speeds of up to 375 mph. But it took more than a decade to get airborne at all. In 2004, as a small crowd looked on in a field near Davis, an updated version dubbed the MX400 shuddered, lurched, and rose a few feet into the air, its rotary engines screaming like a swarm of leaf blowers. After a few minutes, the craft settled back to the ground.

Moller claimed that the Skycar would soon be ready for free-flight demonstrations, but these never materialized. Instead, the Securities and Exchange Commission filed suit against Moller International in federal court for selling unregistered securities, alleging, among other things, that while Moller had touted the Skycar’s promise to investors, “in reality, the Skycar was and still is a very early developmental-stage prototype.” In 2009 his company declared bankruptcy.

Given how little Moller’s machine achieved, it’s remarkable how much favorable press he received. Popular Science featured the Skycar on its cover, and over the years many other magazines and newspapers gushingly endorsed the Skycar as the transportation technology of the future. The concept of the flying car is one of those technological Holy Grails that capture the imagination and fill us with hope. You don’t have to be an aeronauticist to get swept up in enthusiasm for the idea of a flying car.

The dream’s latest incarnation comes courtesy of a team of MIT–trained engineers and MBAs. Called the Terrafugia Transition, the vehicle, like the Aerocar, sports folding wings, but it does Moulton Taylor’s invention one better. Instead of detaching and hooking behind the car, the wings stow themselves alongside the vehicle, so there’s no trailer to pull around. Not only is the concept futuristic-looking, it’s actually flown: The Transition took its maiden flight in 2009, flying for 37 seconds above an airstrip in upstate New York. It went on to fly 27 more times in subsequent weeks, and the press response was adulatory. “The Flying Car Has Arrived (Seriously),” one Forbes headline announced last year, atop a story that repeated Transition’s performance claims: top speed of 115 mph, range of 490 miles, price tag of $279,000—which is still less than the venerable Cessna 172, an aircraft that has been on the market for more than 50 years. More than 100 pre-orders have been placed, mostly by pilots, and the model flaunted its stuff at the recent New York International Auto Show. Still, the FAA has yet to approve the car for flight.

While it’s true that it’s hard to build a flying car and even harder to build one that flies well, what has driven stake after stake into the heart of the concept is economic feasibility. Many novel aircraft designs fail because the price tag winds up greatly exceeding original projections. Can a flying car outperform the alternatives for a reasonable cost? The answer has been, and for the time being certainly will remain, no.

Software designer Austin Meyer is exactly the sort of customer a flying-car builder would hope to snag. He flies often for both business and pleasure, he loves unusual aircraft, and best of all he’s got money to spend. He totally gets the appeal. “When I arrive at my destination at 2 a.m., 40 miles from where I want to be, and my cell phone batteries are dead, that’s when I wish I had a Terrafugia,” he says. But don’t expect to see him lining up to put down a $10,000 deposit. The fact is, he says, that he rarely finds himself stuck at an airport. “It’s so easy to have a rental car, a friend, or a business associate waiting for you with just the smallest amount of planning,” he says.

In return for the ability to drive away from an airport, he would have to pay an enormous price in his aircraft’s performance. “When I’m in my airplane, covering significant miles, I’m really glad that I have plenty of power, a comfortable cockpit, a nice big wing, a control system that’s optimized for flying,” Meyer says. “I don’t want one bit less performance than I have.” And neither, he believes, would many other pilots.

If Meyer’s analysis is correct, then the dream of a practical flying car is a fool’s quest. Then again, if the history of engineering has proven anything, it’s that naysayers can be proven disastrously wrong. Last year, it emerged that no less an aeronautical visionary than Burt Rutan—the inventor of Space-ShipOne, the first private manned rocket to reach space—had dabbled in the flying-car concept. Eight months after announcing his retirement, Rutan unveiled a hybrid gas-electric version he dubbed the BiPod. His plane, like so many before his, got off the ground for only a short hop. But who knows? No one has accomplished the impossible more times than Rutan. If he sees promise in the concept, we may indeed be on our way to the day when cars sprout wings and conquer the sky.