On July 5, 1946, less than a week after the United States detonated an atomic bomb above tiny Bikini Atoll in the South Pacific, a Frenchman named Louis Réard — an automobile engineer moonlighting as a fashion designer — introduced to the sunbathing public the world’s smallest swimsuit. Réard called his creation the bikini, a name inspired, he later said, by the sight of women rolling up their bathing suits in order to acquire a more complete tan.

Two-piece swimsuits had been around for decades before Réard came along. In fact, the concept was even far older than that; Greek urns and mosaics created more than 3,000 years ago depict women athletes wearing two-piece outfits. But Réard’s genius was to devise a garment, out of as little fabric as possible, that one could still legally wear in public. (He marketed his new fashion brilliantly, as well — pronouncing, for example, that a bathing suit wasn’t a true bikini unless both pieces could be pulled through a wedding ring.)

Here, as the weather warms and our thoughts turn to the approaching summer, LIFE.com offers a celebration in pictures of a summer staple that, through the years, has enjoyed — and endured — a dizzying array of permutations while always remaining, unmistakably, itself.

Some of the early photos in this gallery depict two-piece bathing suits that might, at first glance, look like bona fide bikinis. A closer look, however, reveals that while these are, clearly, two-piece suits, there’s far too much material invested in the garments for them to legitimately earn the moniker. After all, one can hardly claim to be wearing a genuine bikini if, say, one’s bellybutton is entirely covered by a swath of nylon, no matter how elegant or tasteful that swath might be.

Bikinis are not for everyone. There are (thankfully!) as many types and styles of bathing suit as there are body types and human temperaments. That said, it remains incontestably true that few sights can evoke that memory-laden concept, summertime, with quite the same visceral punch as the unmistakable silhouette of Monsieur Réard’s ingeniously simple design.