When Angela Ahrendts became the C.E.O. of Burberry, in 2006, the company had an unusual problem: its brand was too blatant. Burberry’s signature pattern, a beige, red, and black plaid, which had formerly been a symbol of exclusivity, was being widely copied—a parody of luxury. It even became associated with a derogatory term in Britain: the “chav,” or working-class delinquent, who wreaked havoc while wearing a knockoff Burberry cap. Ahrendts reined in the brand, taking back some licenses that had been issued to partners in other countries, toning down the plaid, and choosing designs that were sleeker and more sophisticated. For high-end products, subtlety sells.

This week, Ahrendts will join Apple as its head of retail. With her pedigree, she has a chance to solve tech companies’ fashion dilemma: how to create wearable technologies that people actually want to wear. (Ahrendts also has considerable experience in China, where Apple currently has thirteen stores and plans to triple that number within two years.) Although Apple stores are still a big draw, devotees are becoming impatient for new products worth lining up for; on Wednesday, the company said that it sold forty-three million iPhones during its most recent quarter, but the iPhone has been around for seven years now, and Apple’s last major new product, the iPad, was released four years ago. Rumors have been building about an iWatch, which would be Apple’s first attempt at a computer disguised as a fashion accessory. (Apple declined to comment.)

If Ahrendts’s appointment is a signal that Apple is seriously considering building technology into clothes and accessories, a newish category of tech products known as “wearables,” the company wouldn’t be alone in Silicon Valley. Last year, investors put four hundred and fifty-eight million dollars into companies that make wearable products like fitness trackers and baby monitors; last month, Facebook agreed to pay two billion dollars to buy Oculus VR, a virtual-reality technology firm whose Oculus Rift gaming headset looks like a scuba mask with a metal plate bolted on the front. Companies love the idea of wearable technology because that constant data stream would be a bonanza for marketers, measuring what people are doing every second, even while they’re asleep.

Yet—surprisingly or not—customers are reluctant to strap still-bulky computers to their foreheads and wrists. One columnist has noted hundreds of Samsung’s new Galaxy Gear watches for sale on eBay. A recent survey indicated that one-third of Americans who buy a wearable device stop using it within six months. Google Glass raises widespread privacy concerns, partly because its design is so intrusive. And earlier this month, Nike laid off some of the employees working on its FuelBand fitness-tracker bracelet; a Nike design director on the FuelBand project joined Apple last fall, increasing speculation that the two companies will collaborate on a new product.

A major problem with wearable technologies—and one that Ahrendts is in a good position to fix—is that they are too conspicuous. The engineers who design them delight in advertising the fact that they’re wearing the hot new device. But outside Silicon Valley, displaying the cutting-edge equivalent of a BlackBerry holster isn’t chic. When people slip on Google Glass, they resemble the character Seven of Nine from “Star Trek: Voyager,” who had cybernetic implants in her face, signs that she once was subsumed into the dehumanizing Borg.

These sorts of constant reminders that users are plugged in could explain why so many people are reluctant to adopt Google Glass and similar technologies: a new Pew Research Center study shows that more than half of Americans think life will change for the worse if many people wear or implant technologies that constantly provide information about the world around them. (Women are particularly hesitant.) Google seems to recognize this issue. It is partnering with Luxottica, the maker of Ray-Ban and Oakley sunglasses, to design a more stylish Glass.

Ahrendts also seems to understand the potential appeal of integrating tech and fashion. Old-world fashion brands tend to be skeptical of technology—some Parisian couture houses still employ “petites mains” to hand-sew their elaborate gowns—but Burberry, under Ahrendts, embraced it. Two years ago, the company opened a flagship store on Regent Street in London, with the transcendent—or dystopian—mission of “seamlessly blurring physical and digital worlds,” as the company’s Web site put it. When a customer walks toward a handbag or sweater, a radio-frequency I.D. tag embedded in the item cues one of a hundred digital screens throughout the store to play a video with more details about, for example, the fabric or the stitching. A sweeping staircase and gleaming white marble bring to mind a neo-Victorian Apple store. Just substitute trench coats for iPhones.

In the twentieth century, designers took two distinct approaches to imagining the future of fashion. The first approach tended toward metallic, geometric, quasi-robotic styles: think Pierre Cardin’s space suits of the nineteen-sixties, inspired by the first moon landing. The first generation of high-tech wearables look a lot like what those designers predicted. But the designers of the past had another vision, too, and this one could be a big, untapped market: making clothes better serve their original purpose of keeping people warm, dry, and protected. One designer, in 1939, envisioned that decades in the future women would wear an electric belt that would adapt the body to unpredictable weather changes. It’s an attractive idea for anyone who has sweltered on the subway, then spent the rest of the day shivering in an air-conditioned office. Along those lines, a group of M.I.T. graduates have designed a ninety-five-dollar dress shirt that borrows from NASA’s space suits—not the bulky styles themselves, but the technology in their materials—to store heat away from the wearer when it’s too hot outside, then return it when temperatures cool. It isn’t hard to imagine Apple using its technological prowess to weave computers right into clothes, especially if it draws on the fashion sense of Ahrendts and Paul Deneve, the former chief executive of Yves Saint Laurent, whom Apple hired last summer to focus on special projects.

There’s another term for wearable technology that might give a better sense of its future: “intimate computing,” which evokes a product that is sensual and tactile, personal and discreet. Om Malik, a tech blogger who popularized the term, wrote about Apple’s hiring of Ahrendts: “This new intimate computing era means that Apple has to stop thinking like a computer company and more like a fashion accessory maker, whose stock in trade is not just great design but aspirational experience.” That will be Ahrendts’s mission: more Burberry, less Borg.

Photograph: CBS Photo Archive/Delivered by Online USA/Getty.