World War II gave rise to countless innovations that would change American life for decades to come—from the rugged Jeep, to mass-produced penicillin, to the terrifying atomic bomb. But, ironically enough, few U.S. industries were more profoundly affected by the war than the toy business.

Not only were toy and game designers and makers able to take advantage of the latest scientific advances, such as colorful and inexpensive plastics; they also benefitted from two other post-war trends. The baby boom—more than 76 million kids born between 1946 and 1964—offered them record numbers of potential customers. And television, little more than a novelty before the war, soon made it possible to demonstrate the latest playthings to millions of kids at a time. Little wonder that toy sales grew from $84 million in 1940 to $900 million by 1953 and into the billions of dollars in by the early 1960s.

Some early forms of plastic, such as celluloid, had been around since the 19th century. But the 1930s and ‘40s saw the introduction of many more. These plastics became especially important during the war, in part because certain materials, such as silk and natural rubber, became hard to obtain or impossible to produce in sufficient quantities to keep up with the needs of the military. One 1943 experiment resulted in a bouncy substance that proved of little use to the war effort but went on to post-war fame and fortune as Silly Putty.

But while plastics would revolutionize the toy industry, wary manufacturers didn’t make the leap right away, notes Nicolas Ricketts, a curator at the Strong National Museum of Play in Rochester, New York. Parker Brothers, for example, “was afraid to change any details of Monopoly because it was, and continued to be, a cash cow for the firm,” he says.

In addition, toymakers needed time to retool for peacetime. Milton Bradley had cut back its game production during the war to manufacture parts for airplane landing gear and machine guns. Lionel had switched from toy trains to telegraph keys, compasses and other military essentials.

Before the 1940s came to a close, however, plastics were beginning to pop up on toy store shelves, often due to adventurous entrepreneurs willing to take a gamble. The Game of Cootie, in which players race to build colorful plastic bugs, was an instant hit in 1949 and remains popular nearly 75 years later. Its inventor, Herb Schaper, was, in his day job, a Minneapolis mailman.

That same year, the Danish company Lego, founded by carpenter Ole Kirk Kristiansen to make wooden toys, released its first plastic brick. The version that is ubiquitous today came along in 1958.

Mr. Potato Head was also invented in 1949, by George Lerner, an American graphic designer, though it didn’t hit the market until 1952. At first it consisted of an assortment of plastic pieces—eyes, noses, mouths, eyeglasses, etc.—but kids had to supply their own real potato to stick them into.

WATCH: The first season of The Toys That Built America on HISTORY Vault.

Major board game makers took their first cautious steps into the world of plastics by replacing wooden pawns and other small playing pieces with ones made from the new materials. Then some toy designers began to see bigger possibilities.

In 1963, Ideal released the Mouse Trap Game, designed by Marvin Glass & Associates. It added larger plastic objects to the usual cardboard playing surface and is often credited as the first three-dimensional board game. As Ricketts notes, “plastic alone really made the Rube Goldberg aspect of Mouse Trap and its many imitators possible.” (Goldberg was a newspaper cartoonist famous for his drawings of comically elaborate contraptions to perform everyday tasks.)

Glass and his team of designers drove innovation in the toy business, soon following up with other Goldbergian games that took full advantage of plastic’s possibilities. Those included Crazy Clock (1964) and Fishbait (1965), both created, in part, by Dalia Verbickas, one of the rare female game designers of the day.

Glass’ company didn’t manufacture toys, but licensed them to major toy and game makers. Among its most famous creations: Mr. Machine (Ideal, 1960), Rock 'Em Sock 'Em Robots (Marx, 1964), and Operation (Milton Bradley, 1965). None would have existed but for plastic.

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Plastic was not solely responsible for the surge in toy sales in the 1950s and ’60s, of course. The post-war population explosion was another major factor, as was the rapid growth of television and TV advertising. In 1946, only 8,000 U.S. households had a television set; by 1960, more than 45 million did.

As TVs proliferated in American homes, advertisers realized they could now reach kids directly. Toy and breakfast cereal makers became particularly adept at advertising to young consumers; many cereals advertised on television even came packaged with a toy or promised one in return for a number of box tops.

Mr. Potato Head is credited as the first toy to be widely advertised on TV, in the first commercial aimed specifically at children. That year, 1952, maker Hasbro reportedly sold more than a million of them at 98 cents each.

Other toymakers would follow suit, with commercials whose jingles and taglines remain stuck in baby boomers’ heads to this day (whether they like it or not): “Everyone knows it’s Slinky!,” “You sank my Battleship!” and “Trouble, Trouble, that’s the name of Kohner’s ‘Pop-O-Matic’ game.”

As the first wave of baby boomers approached adolescence, toy and game makers had no intention of giving them up as consumers. Some far-sighted companies had already begun to recognize teens as a potentially lucrative demographic during the war, aiming ads at bobby soxers and their male equivalents, notes Stuart Elliott, former New York Times advertising columnist.

In 1966, the year the oldest baby boomers turned 20, Milton Bradley released Twister. Rather than a conventional playing board, it used a vinyl mat with large, strategically placed polka dots. The players themselves served as game pieces, entangling their bodies as the plastic spinner dictated.

Perhaps more than any other game, Twister managed to exemplify all three post-war trends: inexpensive plastic, generational appeal and lively TV ads. Plus, it added a bit of sex—or at least the suggestion of it. In 1967 alone, Twister sold more than 3 million copies.