December 29, 2014, 1:00 PM UTC
Alan Murray
contract Armin Harris
Photograph by Wesley Mann for Fortune

I can’t read enough about Uber. That’s partly because its CEO, Travis Kalanick, is a great show, combining the public relations savvy of Miley Cyrus with the pugnacity of Alec Baldwin. His ride-sharing service now has operations in 53 countries and is valued at $40 billion. Yet the bad-boy boss, who famously called his company “Boober” because of its ability to get him women, acts as if he never left the frat house.

It’s also partly because Uber has become its own genre in Silicon Valley. There’s an “Uber” for almost anything you can imagine these days—including an Uber for laundry (Washio), massages (Zeel), and booze (Minibar). More than $2 billion poured into on-demand mobile-service companies last year, and there’s more to come.

But Uber-mania is also a symbol of something bigger—much bigger. It reflects a profound turn in the way the global economy is organized.

Four years ago I wrote an article for the Wall Street Journal titled “The End of Management.” It looked at the rise of great global corporations in the 20th century, and asked whether they were rapidly becoming obsolete in the 21st because they were too big, too bureaucratic, too slow to adapt.

I pointed out that technology was undermining the very logic of the corporation, as laid out by Nobel economist Ronald Coase in his 1937 article “The Nature of the Firm.” Coase argued that corporations were created because the “transaction costs” of doing business in the open market were too great for complex enterprises, like building railroads, manufacturing cars, or creating telephone networks. But since the dawn of the Internet, Coase’s costs have plummeted, as technology made it easier to transact with workers, suppliers, and customers. If the 20th-century corporation had lost its logic, the article asked, what would take its place?

Uber is the emergence of an answer. It’s a big company and growing larger every day. But more than that, it is supporting, shaping, and creating a new marketplace. It is, truly, a synthesis of firm and market.

And it’s not alone. Companies that combine the characteristics of firms and markets—often called “platform” companies—have been gathering momentum for the past two decades. Think of the Internet retail and auction markets created by Amazon and eBay, the information and media marketplaces created by Google and Facebook, or the music and app markets built by Apple. More recently these new hybrids have extended into human resources, with services like Freelancer and WorkFusion, and even to clean energy, at companies like Sungevity.

“The growth rates of these platform businesses are phenomenal,” says Peter Evans, who is leading a project called “The Emerging Platform Economy” at the Center for Global Enterprise, a think tank founded by former IBM chief Sam Palmisano. “They are redefining the boundaries of the firm.”

The change can be spotted not only at chic tech companies but also at older, more established industrial ones. DuPont CEO Ellen Kullman, for instance, talks of how the process of innovation at her firm has changed in recent decades. “When I got here, the whole model for innovation was internal,” she told me in late December. “Now, between government funding for R&D, collaboration with small companies, little joint ventures, it’s very different,” she says. “Today you have to figure out how to do it in an open and collaborative environment.”

The ramifications of this accelerating trend are enormous. Companies will have to rethink their entire structures. Workers will increasingly become entrepreneurs (see our story “How to approach your own career like an entrepreneur”); supply chains will increasingly become marketplaces. Rapidly growing “platforms” will not only enrich their owners but also empower the users.

So prepare yourself. Your Uber-future is arriving now.

This story is from the January 2015 issue of Fortune.

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