When the Woodville Mall opened, in 1969, in Northwood, Ohio, a suburb of Toledo, its developers bragged about the mall’s million square feet of enclosed space; its anchor tenants, which included Sears and J. C. Penney; and its air-conditioning—seventy-two degrees, year-round! Two years later, the Toledo Blade published a front-page article about the photo-takers and people-watchers who gathered around the mall’s marble fountain, “that gushing monument to big spending and the shopping spree.” The story quoted an anonymous businessman: “The water has a great calming effect on a person, especially when you’ve been badgered all morning.”

This week, Woodville is being torn down. So are countless other malls across the U.S.—so many that there’s a Web site devoted to “dead malls” that are out of commission. In some cases, the buildings have been converted into community colleges, corporate headquarters, or churches. Others, like the Woodville Mall, have become so damaged by water, mold, and asbestos that city officials are glad to demolish them. In January, Rick Caruso, the C.E.O. of Caruso Affiliated, one of the largest privately held American real-estate companies, stood on a stage at the Javits Center, in New York, and forecast the demise of the traditional mall. “Within ten to fifteen years, the typical U.S. mall, unless it is completely reinvented, will be a historical anachronism—a sixty-year aberration that no longer meets the public’s needs, the retailers’ needs, or the community’s needs,” he told his audience, which had gathered for the National Retail Federation’s annual convention.

Part of what’s hurting the mall, obviously, is that, increasingly, people are shopping online. Internet sales reached six per cent of total retail spending in the fourth quarter of 2013, nearly doubling their share from 2006. Some retailers, understandably, are responding by focussing more on the online end of the retail business. Gap, which became synonymous with the American mall, is no longer counting on malls for growth. “Culturally, the business pivoted towards digital,” Glenn Murphy, the C.E.O., said, describing the past year. “Mall traffic, for a number of years, has been slowing down. Whether it continues to decline somewhat over time, I think that’s realistic to assume.” Gap customers now can order clothes online and pick them up in a store. When it opens new stores this year, Gap will focus on Asia; earlier this month, the company launched its Old Navy brand in China.

It’s not hard to imagine the future that Caruso described, in which malls are obsolete: the case for Amazon is pretty strong when the alternative is to crawl through gridlock to a mall, unwittingly park in the space farthest from the store you plan to visit, cringe as toddlers’ shrieks reverberate off the tile floors, and dodge salesmen hawking knockoff perfumes and hundred-dollar curling irons. But Caruso offers an interesting alternative scenario: what if malls reinvented themselves? As any cubicle dweller knows, people like natural light and fresh air and, when deprived of them, feel oppressed. So are people alienated by those older malls, with their raw concrete, brutalist architecture and fretful, defensive air? Developers have a shorthand for this style: the “classic graybox.” In his talk, Caruso flashed grim photos of their façades. He lingered on a picture of a deserted food court; you could practically smell the stale grease. “Does this look like the future to you?” he asked. On Monday, Sbarro, which represents one of the four food groups of mall cuisine, along with Jamba Juice, Panda Express, and Cinnabon, filed for bankruptcy protection for the second time in three years. Court papers cited an “unprecedented decline in mall traffic,” meaning fewer hungry shoppers settling for foldable pizza slices.

It’s worth noting that Caruso has a good reason to pitch the reinvention of malls to developers: outdoor malls are his company’s focus. After his speech, he told me, an executive from one of the largest indoor-mall real-estate companies called to ask if his company could learn more about outdoor malls. But competitors aren’t always so welcoming. In 2011, Caruso’s company cancelled plans for an outdoor mall in the parking lot of the Santa Anita Park racetrack after a legal challenge from Westfield, which owned a nearby indoor mall, and a bankruptcy filing by Caruso’s business partner.

Reinventing malls—and the stores that they house—might not be as straightforward as it seems. For all his shortcomings, Ron Johnson, the much criticized former C.E.O. of J. C. Penney, understood the warnings. He reënvisioned J. C. Penney stores, with their enormous—and enormously dated—open spaces, as places for people not only to shop but to hang out, drink coffee, and surf the Internet. His remodelling blueprints called for a “street” inside each store leading to a spacious “square” that could host yoga classes and other events. But there were two problems with the plan: sales were falling too quickly to support the tremendous renovation costs, and, even if J. C. Penney could have covered the expenses, the stores would have remained stuck in old-fashioned malls. In that sense, Johnson’s previous job running Apple’s retail stores was far simpler—just plunk down a gleaming glass cube on the most profitable shopping streets around the world. Now under new leadership, J. C. Penney has completed only a fraction of the remodelling plans.

Among developers, there’s a tacit acknowledgment that the oldest, sickest malls, the kind that you associate with defunct chains like Waldenbooks and Tower Records, may be left to die. Meanwhile, there’s money to be made from rich people in the U. S. and from everyone in Asia, where malls are not yet passé. In October, Taubman Centers Inc. plans to open a mall anchored by Saks Fifth Avenue in Sarasota, Florida. Though designed as an indoor mall, it will have plenty of brightly lit storefronts that shoppers can enter from the parking lot, darting in and out like fish sampling bait.

But, like Gap, Taubman sees its future in the two malls that it’s developing in China and in a third mall, in South Korea. “There is limited growth in the United States for new supply,” Robert Taubman, the C.E.O., said recently. “We think that, in the long term, China, Asia, represents an opportunity for us to continue to grow this company.” Simon Property Group, another big developer, said in December that it will spin off into a separate company its strip centers and smaller enclosed malls in places like Lima, Ohio (built in 1965), and Lakewood, New York (built in 1971). When the deal is completed, Simon will concentrate on its larger malls, its outlet centers, and on overseas development.

“These indoor malls in the middle of nowhere, which typically supplanted the old Main Street—that’s where it’s an anachronism,” Rick Caruso told me. But he still sees a place for malls elsewhere; after all, people have always needed gathering places, from the Lascaux caves, in France, with their Paleolithic paintings, to the modern-day souks of Marrakech. “Humans have an innate sense of wanting to come together,” he said. “I bet the souk will be there long after Amazon.”

Caruso’s showcase properties—the Grove, in Los Angeles, and the Americana at Brand, in Glendale, California—produce sales per square foot that rank them among the top fifteen malls worldwide. The Americana at Brand also houses more than two hundred apartments and a hundred condo units, so there’s no need for the residents to fight for a parking space. Both malls have a Main Street-meets-Vegas Strip feel, with skyrocketing fountains synchronized to music. The Grove boasts a fourteen-screen, Art Deco-style movie theatre. (Not long after the Grove opened, in 2002, the Los Angeles Times described its “stained-glass streetlights and Easter-colored façades that are neither French nor Spanish but a low-volume Every Europe.”) The malls are busy, well-tended, and vibrant, though they are still malls: a simulacrum of culture, in the same way that the Cinderella Castle at Disney’s Magic Kingdom is a representation of medieval life, without the chamber pots and periodic sieges.