AS I WILTED waiting for the Yohji Yamamoto show to begin last month in Paris, my seatmate, veteran German stylist Klaus Stockhausen—whose knowledge of menswear is as encyclopedic as his sense of humor is robust—ceased repeating unrepeatable jokes and broke into a smile of recognition. It was directed at my sneakers. “Ah, the army shoe! I used to wear them a lot when I started going to shows. German surplus, yes?”

He was quite right. I was sporting the mighty Bundeswehr Sportschuh Halle, also known as the German Army Trainer—a low-key leather sneaker originally created for the country’s military.

What I value most in sneakers is under-the-radar anonymity, a clean silhouette and a competitive price. Spare me Adidas’s Stan Smiths (far too riffed on by Raf Simons and Phoebe Philo) or styles by Common Projects (Common? Absolutely. Yet uncommonly expensive). I thought I’d found an ideal in the Dunlop Volley, a gloriously generic and cheap-as-chips 1970s Australian tennis shoe (just Google it).

A modern GAT aficionado Photo: Melodie Jeng

Then, last January, came my conversion to the German Army Trainer, or GAT, as English-speaking sneakerheads refer to it. It began during a late-night, wine-fueled browse on e-commerce site Mr Porter, where a pair of green faux-lizard sneakers by Maison Margiela were marked down with an end-of-season reduction. They were still a bracing £195 (around $300). But hey, I’d just been laid off. My former employer was cost-cutting, but I’d be damned if I would. Plus, the wine.

In the clear light of day, once DHL had dropped by, this impulse decision proved one to celebrate. I am not a bold dresser. Lizard sneakers sound bold. Yet the simplicity of the upper shape, the raw gum of the outsole and the almost complete absence of branding beautifully tempered any flash. I looked more closely. Inside was a label declaring my new buys replicas of 1970s Austrian sports shoes.

What was that about?

It turned out that the Margiela label was geographically close, but not quite correct. According to most sources, my new lizard sneakers were a riff on the German Army Trainer. Margiela didn’t respond to a request to clear up the Austrian disconnect, though a spokesperson did acknowledge the shoe was based on surplus GATs.

I soon realized the GAT has more conflicting histories than the Caucasus. The GAT design is generally attributed to Adidas, and an Adidas spokesperson confirmed that the company designed a trainer, called the BW-Sport, that the Federal German Army issued its men and women in the ’80s and ’90s. However, a spokesperson from the Bundeswehr History Museum in Dresden said they only had records that the design was made by Puma—the company started by Rudolf Dassler after he split with brother Adi Dassler (founder of Adidas)—at least in the testing phase. Another discombobulating twist: Puma told me it has no records of a shoe made for the government. And—pah!—forget studying a surplus sneaker for clues. Since they were made for a government agency, there is zero branding.

Up in Army // Fashionable Riffs on the Military Trainer From top: Sport Trainers, $255, epauletnewyork.com; Leather Replica Sneakers, $650, Maison Margiela, 212-989-7612; Svensson Army Sport Trainers, $352, Goose Barnacle, 718-855-2694 Photo: F. Martin Ramin/The Wall Street Journal, Styling by Anne Cardenas

What is clear is that before the fall of the Berlin Wall, in 1989, the sneakers were issued to a standing force of more than half a million members. When the force was downsized, the shoes quickly seeped into the civilian realm. First, they became widely available in surplus stores across Europe. The genuine article is still easily found on eBay, Amazon and various other sources. (Once I understood the origins of my Margielas, I headed to eBay and bought a seemingly boxfresh pair of originals for 45 euros, around $49, postage included—the pair Mr. Stockhausen spotted on me in Paris.)

In 1998, it was Maison Margiela founder Martin Margiela who inducted the shoe into the high-fashion ranks. The creative recycling of pre-existing items—the elevation of the mundane—was a central tenet of the Belgian designer’s practice. For the spring 1999 presentation of his “Artisanal” line, he showed models shod in BW-Sports, purchased at surplus shops, washed and given new insoles and laces.

A few years later, his company started producing the shoe itself. It’s almost the same pragmatically anonymous shape as the BW-Sport but made in an increasingly elaborate variety of luxe fabrications and finishes—paint-splattered, fluorescent, even woven in straw.

“ This shoe has more subtly conflicting histories than the Caucasus. ”

Over the past decade or so, the GAT has gone steadily viral. Dior Homme, under creative director Hedi Slimane, produced a version called the B01 in the mid-aughts. New York menswear label Epaulet recently introduced a version that’s an excellent halfway point between Margiela and surplus. Then there’s a pleather iteration by a Japanese label called YMCL KY that sells for a trifling ¥3,800 (around $31). Even Adidas has produced versions: the BW Army Clean, made in 2008, and the Resplit Lo, from 2010.

One relatively enduring GAT reboot comes from Svensson, the Malmö, Sweden-based club collective turned clothing brand. Co-founder Matias Alfieri said their 300 euro version, with a slightly thicker Margom sole, has sold consistently well since its introduction seven years ago. “I don’t know if it sounds good to say it,” added Mr. Alfieri, “but I prefer our version to the original.”

Heresy? Of course not. The GAT, like many other co-opted military items, has become a template to be reinterpreted. And via fashion designers and GAT geeks like myself, this shoe has become a paradigm of sneakerdom—and one with wide appeal. Last week I interviewed Manolo Blahnik, arguably one of the world’s greatest shoe designers. I wore the Margielas, even though he’s known to detest sneakers. Within a minute of our meeting, he glanced down, paused, and then pronounced: “Oh! How pretty they are!”