The Dreamliner is a plane that many people never expected to be built, especially by Boeing ba . A sizable camp believed that Boeing, the outfit that ushered in the Jet Age, no longer had the right stuff to build an entirely new airliner. Happy to profitably stretch and tweak versions of its family of such planes as the 737 and 747, Boeing had seen its day of defining the direction of commercial aviation. Since 1994, when the last all-new Boeing model, the 777, took to the sky, Boeing’s chief rival, Airbus, was calling the shots in aerospace innovation.

The Dreamliner, also known as the 787, is Boeing’s gambit to take back its title, not only as the leader in overall sales of commercial jets, but also as visionary for an industry. With its carbon-fiber skin, the Dreamliner is the first commercial jet that has more in common with a B-2 stealth bomber than the riveted aluminum tube in which passengers currently fly. Lighter, quieter, and more comfortable, the 787 is designed to fly farther on less fuel than any existing airliner. It is the future.

That is, as soon as it’s delivered. Since it was made available for sale in 2003, Boeing has sold 892 Dreamliners to 57 customers around the world. At a list price of $162 million, that’s worth about $145 billion. Yet not a single Dreamliner has flown, and the 787 is more than a year behind schedule. One reason is that Boeing has been innovative to a fault. When it decided to engineer a new aircraft, the company also decided to engineer a new manufacturing process. That process includes dozens of partners around the globe that build and preassemble big pieces of the plane. Boeing’s job is to manage this far-flung supply chain and to make sure the parts fit together flawlessly on the factory floor in Everett, Wash.? That, too, is the future, but only if Boeing can figure out how to do it right. Most of the delay on the 787 can be traced back to a handful of suppliers that were not able to ramp up production fast enough on parts ranging from small metal fasteners to whole sections of the aft fuselage.

With customers growing impatient, Boeing’s reputation is on the line. Says Pat Shanahan, the 787 project director: “How well we do on this will define the fundamentals for manufacturing commercial planes in the future. That’s the big bet.” For this exclusive photo essay, Fortune was given unprecedented access to the Dreamliner’s manufacturing process around the world, from initial twists of carbon fiber to finished wings. In that journey from factory to factory, a clear message emerged. While the engineers and the assemblers are keenly aware of the disappointment and consequences of the delays, there is an unshakable belief that the 787 will fly soon—and some day will be acknowledged as the plane that charted the next age of commercial aviation.

▸ Barrel Roll

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In Wichita, a nose section (note cockpit window frame) slowly twists as workers at Boeing subcontractor Spirit AeroSystems inspect the interior structure. The barrel, built in one piece, was formed around a mold with miles of precision-applied carbon-fiber ribbon.

▸ Spinning the Skin

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A technician at Toray Industries in Fredrickson, Wash., makes sure carbon-fiber strands coming off 300 spools are lined up correctly before applying a layer of epoxy resin. (Each of the strands entering the machine contains 24,000 filaments.) The finished composite sheets, which have the consistency of fruit leather, are laid down in alternating patterns on a piece of the plane like this nose section, then baked in an autoclave. The resulting composite is stronger than steel and virtually dent-proof.

▸ Sculpted Wings

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Two workers at Mitsubishi Heavy Industries in Nagoya, Japan, apply composite shims to the Dreamliner’s central wing box. The wingspan is 197 feet, or about 25% longer than a similar-sized plane, which increases lift and reduces drag. Thanks to the 3-D modeling used for engineering and the ease of contouring the composite material, the wings are also more graceful than any aluminum plane’s, with subtle curves that have a strong resemblance to a bird’s wings.

▸ Built-in Comforts

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Kawasaki Heavy Industries in Nagoya, where a forward section of the fuselage is built. Because the outer wall of the plane is so strong, the cabin can be pressurized more than in older jets. At cruising altitude, passengers will feel as if they’re at only 6,000 feet, about the height of Colorado Springs. And because the composite skin doesn’t corrode the way aluminum does, airlines can increase the cabin humidity to more comfortable levels.

▸ Main Assembly

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Each plane on the line is numbered. Dreamliner No. 2, seen from behind, is prepped to receive its vertical stabilizer at the factory in Everett, Wash., the world’s largest building by volume. Unlike the massive, fixed structures used to build other planes, all the tooling for the 787 is mobile, bringing parts together under guidance from a global positioning system. Boeing hopes the system will reduce final assembly to three days. A comparable aluminum plane requires four months to build from scratch. In the plant every single tool is accounted for, since a torque wrench left in a wing could mean disaster. Above, Petru Radu, riding bike No. 808, makes sure all the tools that go out on a shift come back in.

▸ Technology at Work

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Lavatories are Space Age too. Made at Jamco in Murakami, Japan, each of the 787’s bathrooms is a sandwich of carbon fiber and honeycomb paper that weighs a wispy 170 pounds. What travelers will notice, though, are the touch-free faucets and toilets, operated by motion sensor. The flight decks where the pilots will work, built in Wichita, will be outfitted with a bank of LCD screens and “digital flight bags,” containing all the navigational information pilots used to keep on paper, rather than the usual forest of dials and knobs.

▸ Vital Components

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Customers have two choices for engines: GE’s GEnx or Rolls-Royce’s Trent 1000. Both are lighter and quieter and pollute less than previous models. A Rolls mechanic (above), framed by hydraulic pumps and oil lines—that’s the 28-quart oil tank with the yellow cap—checks the fan blades, which at their tips move faster than the speed of sound. The 787’s main landing gear (below), supplied by French company Messier-Dowty, has titanium beams forged in Russia, brake parts from Italy, and a cylinder made in Canada of steel with a tensile strength so great that a matchstick-sized piece could pick up a car.

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▸ Everybody Get on Board

1. Executives of Japan’s ANA airlines, which put in the first order for 50 planes, visit Boeing’s Dreamliner Gallery in Everett, Wash.

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2. Pat Shanahan, Boeing’s head of the Dreamliner project, has battled delays by sending manufacturing experts to supplier plants around the world. He has promised the 787 will fly by the end of 2008.

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3. Chief pilot Mike Carriker, in the flight deck he helped design, will make the first test flight. “Take off, land, and stop,” he says of his plan. “And make sure I get a picture in the air.”

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4. When you pay $162 million for a plane, you get to pick your fabric colors (and your seats, coffee pots, and mood lighting), all presented by Boeing employees in the Dreamliner Gallery.

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5. Tucked above the main cabin of the 787 are bunk rooms for pilots and flight attendants.

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6. Take a 747, raise the roof about ten feet, and you have the Dreamlifter, a flying freight car that shuttles wings and other parts from all over the world for assembly in Everett.

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A version of this article was originally published in the May 5, 2008 issue of Fortune with the headline “Boeing’s Big Dream.”