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It’s a lot to ask from one small piece of fabric. Conceal but also entice. Not to mention enhance or minimize, flatten or uplift. Contained in just 2 cups and bit of strapping are the vanities of millions of women, not to mention the fantasies of countless men. We just got a recent reminder of those fantasies when an Australian banker was caught ogling pictures of Victoria’s Secret model Miranda Kerr on live TV.

The odds a sexually active woman picks at least one occasion to wear something sexy for her partner are 1 in 1.41 (70%). There’s no better occasion than Valentine’s Day, but for the guys about to venture into Victoria’s Secret to buy something red and lacey for their Valentine, a bit of advice: you might want to factor in some comfort along with sex appeal.

It was a personal revolt against her own very uncomfortable corset that spurred 19-year-old Polly Jacob of New York to whip together the first modern brassiere in 1914. Frustrated that her bulky undergarment was ruining the lines of her delicate evening gown, Jacob announced her intention to go without, prompting her scandalized maid to point out that the eyelet fabric would leave Jacob’s nipples exposed. Undeterred, Jacob quickly stitched together two pocket handkerchiefs and some ribbon, while conceding the point that no one should suspect an unmarried woman was possessed of breasts.

Those two hankies caused an immediate sensation, and Jacob’s friends—and soon total strangers—began to clamor for their own homemade brassieres. Before the end of the year, Jacob had obtained a patent, and fearing the invention would deprive them of business, the Warner Brothers Corset Company promptly paid her $1,500 to acquire the rights. Those rights have since been valued at $15,000,000.

The war effort accelerated the push to substitute bras for corsets. When the US War Industries Board calculated that American women required 28,000 tons of metal for their corsets—“enough to build two battleships”—patriotic American women were encouraged to embrace the bra.

Over the years, bra shapes have changed as different breast profiles have gone in and out of fashion. During the flapper era, the vogue was to appear flat. By the 1930s, womanly curves had made a comeback, and the Maidenform Company had pioneered individual cup sizes. By 1937, Warner was offering the A, B, C, and D cups women are familiar with today (thanks to implants, the range has recently expanded to cover AA all the way to JJ). The late 1950s and early ‘60s brought us the “sweater girl” bra, torpedo-shaped cones that were stiffened into sharp points by circular stitching. Today this shape is best enjoyed by watching the television show Mad Men.

Alas, nature did not give every woman either the shape or the substance to fill out such spheres, and at a 1955 conference of underwear manufacturers in Great Britain, a public estimate was given that 3 out of 4 women had resorted to wearing falsies—some of them inflatable devices. In fact, breast enhancers have been around since the 1850s, the earliest made of wire or rubber. Almost a century and a half later, in 1994, the first Wonderbra® was marketed in Britain, and suddenly even flat-chested women had cleavage. Seven years later, the Air Wonder model promised every woman “high altitude cleavage” through an old idea—special shaping enhanced by air pumps.

Today, 16 billion dollars a year are spent on brassieres. And there are still plenty of new ideas, and new patents—sports bras with built-in heart monitors, bras with radiation detectors in case of nuclear war, and after 2001, special wireless underwire bras, designed not to set off airport security alarms.