On a recent trip to Australia, Fred Noe, the master distiller at Jim Beam, stopped by a liquor store in a small town outside Sydney. In the city, Noe had seen hundreds of people line up to get his signature on a bottle of bourbon. “My guys said, ‘Fred, you’re a rock star!’ And I said, ‘Yeah? Where are my groupies?’ ” But even here, in the Australian countryside, dozens of bourbon fans had shown up to greet him — groupies included. “A lady asked me if I would come outside and sign the hood of her car,” he says. “I took a Sharpie and wrote ‘Stay on the Beam’ on the hood of her Ford Falcon. Another lady wanted me to come home with her and sign her pool table, but the sales manager said, ‘No way.’ ”

Noe chuckled, but he’s used to it. American whiskey has never been hotter, and that has made the man behind Beam an international celebrity. Noe is the great-grandson of Jim Beam and the seventh member of his family to serve as the company’s master distiller. But while his forebears spent most of their time laboring over stills in Kentucky, he’s as likely as not to be judging a cocktail competition in Moscow or meeting with executives in Beijing. “That is something I never dreamed in my entire life, going to Russia or China,” he says. “Those might as well have been the moon.”

A decade ago, the American whiskey industry was flat on its back, having suffered decades of weak sales and underinvestment. Today, though, bourbon — the corn-based, barrel-aged spirit that accounts for the vast majority of the whiskey made in America — is everywhere, from Mad Men to the wet bars of C-level office suites, feeding a global ecosystem of tourism, whiskey bars, cocktail competitions, and craft distilleries. The most coveted drink on Wall Street is no longer a Screaming Eagle Cab or a 40-year-old Glenfiddich, but the 23-year-old bourbon from Pappy Van Winkle, which is so rare that it can retail for up to $3,500.

“I like that it’s a bit sweeter, whereas I don’t really like the smokiness of Scotch,” says Ian Bremmer, the founder and president of the Eurasia Group and just one of the many young, globetrotting executives turning to bourbon. “It’s like the difference between American reds and French reds. The French are smoky and oaky, while Americans do fruit bombs — which, done well, are really nice.”

In absolute numbers, the bourbon industry’s $8 billion in global sales is relatively modest. (The Coca-Cola company alone has 16 drink brands with annual sales above $1 billion.) What’s extraordinary is the growth — and the fact that bourbon’s popularity appears to have come out of nowhere. According to Euromonitor, domestic whiskey sales have soared by 40% in the past five years — NASCAR-fast numbers in a sector where good growth often means 2% or 3% a year, and a revolution for a spirit whose sales declined almost without a break for 30 years. Things are even better abroad. In 2002, American distillers exported just $376 million in whiskey; by 2013 that number had almost tripled, to $1 billion, according to numbers released this month by the Distilled Spirits Council of the United States.

Growth is particularly strong in the so-called super-premium category — that is, the brands that cost about $30 or more, like Maker’s Mark — where sales were up 14.4% in 2012 alone, according to the Distilled Spirits Council. “We have trouble keeping bourbon in stock that’s over $50,” says David Othenin-Girard, a spirits buyer for California’s K&L Wines. “It’s just flying off the shelves.”

As if to underline bourbon’s global cachet, last month Suntory, the Japanese spirits and beverage giant, announced a surprise $16 billion bid for Beam Inc., which owns the Jim Beam family of whiskey brands as well as Laphroaig single-malt Scotch, Sauza tequila, and Courvoisier cognac.

“This is probably the best time to be in bourbon since Prohibition,” says Tim DeLong, the managing director for global whiskeys at Brown-Forman, which makes Jack Daniel’s and Woodford Reserve. The industry has responded by investing some $300 million in new capacity over the past two years. Drive through the hills outside Kentucky whiskey meccas like Bardstown or Lawrenceburg and you’ll see new, five-story aging warehouses sprouting like boozy mushrooms in the bluegrass.

It’s not just the big guys who are making bank. Hundreds of startup craft distilleries have opened in the past five years. “Every year I’ve been in operation I haven’t been able to make enough,” says Darek Bell, the co-founder of Corsair Artisan Distillery in Nashville.

But the sudden popularity of bourbon raises an inevitable question. While some trends turn into new normals, others follow the law of gravity and decline almost as fast as they rose. Mad Men won’t always be on TV, after all. The whiskey industry has been in bubbles before, when spikes in demand drove up production, only to have sudden changes in consumer preferences pull the floor out from under it. Fortunes were ruined, and venerable brands disappeared, leaving the industry in a shambles. Can distillers avoid the same fate this time around?

To see the remains of the last bourbon boom, head south from Frankfort, the Kentucky state capital, along McCracken Pike. Tucked around a bend behind a chain-link fence sits what look like the ruins of a Rhenish castle, complete with decaying battlements and medieval turrets. This is the Old Taylor distillery, built by the legendary Kentucky distiller and politician E.H. Taylor in the late 19th century and once home to one of the most venerable brands in American whiskey.

Old Taylor survived Prohibition (it was acquired by National Distillers, a forerunner of Beam Inc., in 1935); it also survived World War II, when liquor production was completely shut down so that distilleries could make industrial-grade alcohol for the military. In fact, brands like Old Taylor prospered in the postwar era, when whiskey and soda was the national drink. “The 1950s was the golden age of the Kentucky bourbon industry,” wrote the historian Michael R. Veach in his book Kentucky Bourbon Whiskey. “There were no restrictions on production — beyond sales projections.”

But that was the problem. Whiskey is unlike most spirits — or most any consumer good, for that matter — in that production cycles are measured in years, not days or weeks. No matter how efficiently a distillery mills its grain or ferments its mash, a four-year-old bourbon has to sit in a barrel for at least four years. That means production levels are based on projections far into the future.

In the 1950s and ’60s, the whiskey industry predicted endless growth. Distilleries were filling barrels as fast as they could make them, socking away a million or more a year. In 1967 there were 8 million barrels of whiskey asleep in Kentucky warehouses. Then the bottom fell out. Like everything else in America, consumer taste in alcohol went through a paradigm shift in the 1960s and early ’70s. Between 1960 and 1975 whiskey’s share of the liquor market dropped from 74% to 54%, while the “whites” — vodka and unaged rum and tequila — climbed from 19% to 35%.

If the 1950s were a party for the bourbon industry, the 1970s and ’80s were the hangover: Jobs disappeared, profits plummeted, and major distilleries were closed or sold off, including Old Taylor and Stitzel-Weller, which was founded by Julian “Pappy” Van Winkle. (Old Taylor went dark in 1972; Stitzel-Weller held on until 1991.)

But rather than accept a niche market position, distillers downshifted, often blending high-quality, well-aged bourbon with neutral spirits to create a lighter, blander whiskey designed for mixing into cocktails, which they sold on the cheap. The result was a vicious circle: A focus on down-market brands reinforced bourbon’s uncool image, which drove young consumers further away. “In the ’70s and ’80s bourbon was your father’s drink, or worse, your grandfather’s drink,” says Eric Gregory, the president of the Kentucky Distillers Association.

“Analysts had pretty much consigned us to the great whiskey store in the sky,” says Max Shapira, the president of Heaven Hill Distilleries Inc., which makes bourbon brands like Evan Williams (no relation to the Twitter co-founder). Many in the industry were similarly pessimistic: In 1999 distilleries put just 450,000 barrels away, 60% less than during bourbon’s heyday.

The roots of today’s bourbon renaissance go back to 1984, when Elmer T. Lee, who manned the radar in a B-29 bomber during World War II and later became the master distiller at the George T. Stagg Distillery — now called Buffalo Trace — created Blanton’s, the world’s first single-barrel bourbon. (In a single-barrel whiskey, each bottle contains whiskey from just one barrel, thus making it a purer expression of the distiller’s skill.) The distillery was in a bad way; the 250 people who worked there when Lee began, in 1949, had shrunk to just 50. In the whiskey equivalent of a Hail Mary pass, Lee bet that a super-premium whiskey could reverse bourbon’s downward-spiraling image, much in the way that single-malt whiskey had recently made Scotch such a hot commodity.

Other distilleries followed. In the late 1980s, Beam began rolling out its small-batch collection, including brands like Knob Creek and Basil Hayden’s. In 1996, Brown-Forman introduced Woodford Reserve. These whiskeys were older, higher proof, and more complex in flavor. Critics loved them — but the bottles didn’t move. Gregory, who worked at a Lexington liquor store while a student at the University of Kentucky, recalled that the only people buying Blanton’s were Japanese executives passing through on their way home from the nearby Toyota plant. As late as 2008, when David Driscoll joined K&L Wines as a spirits buyer, “bottles of Pappy just sat on the shelf.”

What a difference six years can make. Today those same Pappy bottles, which retail for less than $200 for the 20-year-old expression, are as rare as turkey teeth and can fetch more than 10 times that amount on the secondary market. Last year a thief made international headlines after stealing $25,000 worth of the bourbon from the Buffalo Trace Distillery, where it is made under contract. The case is unsolved.

Pappy isn’t alone. From 2002 to 2007, bourbon sales grew by a lackluster 2.3% a year, according to Euromonitor. But over the next five years that rate almost tripled, averaging 6.75% a year. And the bulk of that growth has been at the upper end of the market: Over the past five years, reports the Distilled Spirits Council, sales of “value” bourbon — priced below $15 — have grown just 13%, while super-premium bourbons, the category that Elmer T. Lee pioneered a generation ago, are up 97.5%.

The boom is great news for Kentucky, where people are flocking to experience bourbon in its native habitat. Last year 600,000 people visited the distilleries around the state, hoping to get a glimpse of Fred Noe or another rock-star master distiller. “The idea of getting to hang out with [Wild Turkey’s] Jimmy Russell — when you look at people’s faces, it’s like a religious experience,” Gregory says.

The sudden shift has even caught industry analysts by surprise. “I’ve been covering whiskey for 20 years, and this is the first time I’ve seen significant growth in bourbon whiskey,” says Donna Hood Crecca, the senior director of the Adult Beverage Resource Group at Technomic Inc., a research firm.

What happened? Behind the sales numbers is a dramatic shift in bourbon’s image. Authenticity is everything today, and bourbon, with its long history and made-in-America honesty, is as authentic as it gets. Vodka and gin can be made anywhere, and are — but bourbon has deep roots in American history, from the settlers who first set up stills in Kentucky in the late 18th century through the pioneers who carried it farther west after the Civil War.

That authenticity has in turn attracted celebrities to the drink, who have become bourbon proselytizers. Famous chefs like Sean Brock and David Chang tout the virtues of amber-hued Pappy Van Winkle. Anthony Bourdain, moonlighting as a screenwriter for the HBO series Treme, worked Pappy into a scene; Vince Gilligan, the creator of Breaking Bad, did the same with a bottle of WhistlePig, a rye whiskey bottled in Vermont (rye is like bourbon, except that its primary grain is rye, not corn). The actress Mila Kunis recently signed on as a Jim Beam brand ambassador.

“It used to be that bourbon was the older-guy-smoking-his-cigar kind of profile,” says Greg Fischer, the mayor of Louisville, whose city has benefited enormously from the bourbon boom. Last year tourists from all 50 states and 50 countries came through town to visit distilleries; while in Louisville, they spent millions on local restaurants, bars, and hotels. And it’s not just retirees making the trip, says Fisher. “Now it’s younger people, hipper people” — attracted to it, ironically, because it recalls an older era, a time somehow more authentic than ours.

That rugged authenticity also explains why whiskey has taken off among craft distilleries. In 2000 there were just 24 craft distilleries across America; today there are more than 430, the majority of which make or are planning to make whiskey. Their entry is, in turn, driving innovation among the big players. “They’re breathing life into the American whiskey industry,” says John Hansell, the editor of Whisky Advocate. Among those innovations are flavored whiskeys, which have opened up corners of the consumer market, like Hispanics and women, long overlooked by whiskey distillers.

It also helps that other spirits, like vodka, seem to have run their course. Though the market for vodka is more than three times larger than that for bourbon, its growth has slowed in recent years. “There’s a cyclicality to it that is generational; think of the Chardonnay-drinking baby boomer,” says David Fleming, an analyst for M. Shanken Communications, which publishes research and magazines about the beverage sector. “America was always a spirits-drinking nation, and in a way, baby boomers were an aberration.”

Plus, unlike Scotch — which is made with malted barley and is often distinguished by a heavy smokiness — bourbon is made for more than sipping. “It’s a very versatile product,” says Hansell. “It’s for sipping on the rocks or for mixing into cocktails. And it’s great for pairing with food.” The cocktail part is key — many of the most popular mixed drinks today, like the Manhattan and the Old Fashioned, are bourbon-based.

Then there is bourbon’s pocketbook appeal. “Getting into single malts in a serious way costs a lot of coin,” says Kris Comstock, the brand manager for Buffalo Trace. “A bottle can be in the hundreds, even thousands, of dollars. But you can get into bourbon and have a nice collection for a low price.”

The bourbon boom isn’t just a domestic phenomenon. For years American whiskey, led by Jack Daniel’s (technically not a bourbon but a closely related “Tennessee whiskey”), had a small hold on global consumers, concentrated in developed markets like Germany and Australia. “Until three or four years ago, bourbon was suffering a decline,” says Jeremy Cunnington, a senior alcoholic-drinks analyst at Euromonitor in London. Now, suddenly, it’s taking off. “There is an absolutely huge scope for expansion.”

In developed markets the new demand is coming from the same sort of young, adventurous consumers who are packing whiskey bars in the U.S. “The taste profile of bourbon, which is sweeter because of the mash bill, has been really interesting to consumers in other countries,” says Chris Bauder, the general manager for whiskeys at Beam Inc. Bourbon exports to France, for example, more than quadrupled, to $111 million, in 2012. (It also helped that recent trade negotiations with the European Union and other countries have essentially zeroed out tariffs on most spirits.)

In Japan, where bourbon has been a big seller since it hit the country’s bars during the postwar American occupation, exports have nearly doubled in 10 years. That may explain why Japan’s Suntory jumped ahead of a number of European suitors, including France’s Pernod Ricard, to bid for Beam last month — offering to pay Beam stockholders $83.50 per share, a 25% premium over the stock’s then-market price of around $67, in addition to assuming some $2.4 billion in company debt.

Demand is growing even faster in developing countries, where newly flush consumers are gobbling up anything American. Bourbon exports to Mexico grew by 6,591% over the decade, to $13.5 million. Even many Muslim countries have been thirsty for bourbon: The United Arab Emirates saw exports go from $970,000 in 2002 to $8.2 million a decade later. “I went to Dubai last year with Jeff [Arnett, the master distiller at Jack Daniel’s],” recalls Rick Bubenhofer, the director of PR at Brown-Forman. “Here was this Arab country, and we had 700 bartenders show up. We had to pull him off the stage, they were mobbing him so much for an autograph.”

All this growth, and the subsequent pressure on supply, may be a good problem for distillers to have, but it is still a problem. “We only have as much [10-year-old bourbon] available as we made 10 years ago,” says Comstock. “We’ll continue to make more, but it won’t help today.”

In response, distillers have gone on a building spree. Brown-Forman, which owns Jack Daniel’s, is spending $100 million to expand its distillery in Lynchburg, Tenn., $30 million to expand its Woodford Reserve distillery in Kentucky, and another $60 million on a new cooperage, or barrel factory, in Alabama. Maker’s Mark, which is owned by Beam, recently committed $8.2 million to expanding its supply. And Heaven Hill has increased the capacity at its main distillery by 50% and added four new warehouses.

Distillers are also pouring whiskey into barrels as fast as they can. For the first time since 1977, distillers are sitting on nearly 5 million barrels, significantly more than one barrel for every man, woman, and child in the state of Kentucky.

But still it’s not enough. And so corners are being cut. Last year Maker’s Mark drew brickbats after it announced that it would reduce the proof on its signature expression from 90 to 84 (proof is twice the alcohol percentage) as a way to make supplies last (it backed off). Others, like Buffalo Trace and Heaven Hill, are dropping age statements on some brands so that younger whiskeys can be mixed in.

Bourbon’s return to the hot-warehouse mentality of the 1950s and ’60s raises an uncomfortable question: How long can the boom last, and if it ends suddenly, will distillers once again be caught short? “Everyone talks about getting to the end of a bubble, not just in American whiskey, but in all whiskey,” says Hansell. “We’ve been through this before, and it could happen again.”

Anyone who was in the Texas oil business in the 1970s knows how easy it is to mistake a temporary boom for a permanent state of expansion. And while those in the whiskey industry are uniformly optimistic, many on the retail side are skeptical. “I’m very worried about it,” says Michael Dolega, who oversees whiskey for BQE Liquors in Brooklyn. Distillers are running out of quality, well-aged bourbon, he says, and eventually consumers are going to grow tired of the hype and move on. “I don’t know when, but the bust is coming.”

Still, Hansell added, this time it might not be so bad. Most distillers have diversified portfolios — wine, tequila, cognac, and vodka — that will help buffer against a sudden turn south in the whiskey market. And whereas the previous whiskey boom was mostly domestic, the global nature of the current expansion makes it unlikely that a correction will affect every market at the same time.

If a bust comes, it will hit the craft sector hardest. Like any new industry being flooded by startups, only a relatively small number have the right combination of quality, talent, and management acumen to make it. Many people compare the present craft boom to craft beer in the late 1990s. “It got to where everyone and their brother was making beer,” says Hansell. Then, when the recession of the early 2000s hit, hundreds of those newbie breweries couldn’t stay afloat. “There will be a similar shakeout in distilling,” he says. Then again, the shakeout in brewing cleared the field for stronger craft producers, like Sierra Nevada and Dogfish Head, to expand rapidly in the subsequent decade.

For now, though, the industry is partying like it’s 1959 — and trying its best to forget what came afterward. Bourbon sales may be just getting back to where they were before the Great Bust, but its position in the American psyche is a much more solid, central one. “Bourbon is not just a drink anymore but a part of the culture,” Gregory says. “I really believe we’re in the second or third inning of this thing.”

Clay Risen is an editor at the New York Times and the author of American Whiskey, Bourbon, and Rye: A Guide to the Nation’s Favorite Spirit. His next book, The Bill of the Century: The Epic Battle for the Civil Rights Act, will be published in April.

This story is from the February 24, 2014 issue of Fortune.