She has had more than 250 careers, lived in over 50 different houses and has a shoe collection that would make Imelda Marcos envious. Now, at the age of an eternally youthful 65, Barbie has taken over the Design Museum, filling its galleries with a behind-the-scenes look into the creation of her pink plastic universe.

If you’re still reeling from the tidal wave of Barbiemania unleashed by last summer’s hit film, don’t turn away just yet. This exhibition delves deeper than Greta Gerwig’s movie managed, exploring the fashion, architecture, design and body-image stories behind the world’s most popular doll, revealing her role as a mass-produced mirror of contemporary culture over the last six decades. It is a 29cm-tall tale of shifting attitudes to women’s career choices, domestic tastes, vehicle design, waist-to-hip ratios, furniture fads, hairstyles and more, as viewed through the savvy eyes of America’s most cunning marketeers. It shows how preteen aspiration has been cleverly honed, manufactured, packaged and monetised. And it reveals the unlikely influence that Barbara Millicent Roberts – profession: teenage fashion model – has had on the world around us.

If our homes are a reflection of ourselves, there is nothing more revealing of Barbie’s inner psyche than the evolution of her Dreamhouse over the years. The first such toy abode was launched in 1962, three years after the doll appeared on store shelves, as a canny way to get people to buy more accessories – and more dolls to fill it. But it also became a powerful symbol of independence. At a time when women were denied mortgage applications on the basis of their sex or marital status in the US, Barbie owned her own flatpack home, complete with a carrying handle for easy portability.

It might have been made of cardboard, but it was a chic one-room bachelorette pad, decked out with sunny yellow walls, a TV, record player, well-stocked bookshelves, wardrobe, single bed, varsity pennants – and no kitchen in sight. While other children’s toys were geared towards teaching future wives domestic skills, this was very much a place for a well-educated single woman to have fun on her own. Ken’s presence was confined to a framed portrait on the shelf.

Barbie’s urban aspirations grew in the 1970s, in the form of the Townhouse: a tower-like residence conceived as a maximalist fantasy, with sleek modernist furniture mixed with traditional floral fabrics, ornate woodwork and houseplants, reflecting the height of 70s style. Barbie embraced her more rural ambitions in 1978 with a breezy A-frame house, which curator Danielle Thom credits partly to the influence of Frank Gehry, who designed an (unbuilt) home for Mattel founders Ruth and Elliot Handler. It was the last gasp of modernity before Barbie’s reactionary turn of the 1980s and 1990s, when the Dreamhouse ballooned into a sequence of inflated McMansions with ever higher price tags, replete with classical columns, rococo furniture and chintzy fabrics – signalling the dawn of pink everything.

“This was the socially conservative era of Reagan and Thatcher,” says Thom. “We see Barbie’s world become much more suburban and opulent, reflecting upper-middle class aspirations of the time.”

Barbie’s wardrobe follows a similar path. Her clothes evolve from 1950s swimwear and kitten heels, to hippy California surfer chic (to match her campervan lifestyle of the 1970s), to power-dressing shoulder-padded business suits of the 1980s and lavish ballgowns worthy of the Met gala. It is a shift reflected in the advertising, too, with TV commercials moving from good-times independent adventure Barbie to a Barbie whose sole ambition in life appears to be to ensnare Ken. A hilarious 1980s advert for Peaches n’ Cream Barbie shows the doll engulfed in a puffy cloud of peach fabric, wrapped in a seemingly endless stole, giving her the look of a walking meringue – as Ken looks on in his tuxedo, mesmerised. “What a look,” sings the voiceover, “Ken is hooked!”

Kenneth Sean Carson’s name might never appear on the Dreamhouse title deeds, but there is a small section dedicated to Barbie’s dream man in the show. Just like the Barbie doll, it shows how attitudes to masculinity have changed over the decades, from the dawn of chiselled-jaw, broad-shouldered New Good-Lookin’ Ken of the 1960s to the decidedly ambiguous Earring Magic Ken of 1993. Dressed in a pink mesh T-shirt, sleeveless lilac PVC top and assorted silver jewellery, he is the best-selling Ken doll of all time – primarily thanks to an enthusiastic audience of adult gay men.

The big shiny ring on a chain around Earring Magic Ken’s neck prompted particular mirth, although Mattel’s then marketing manager, Lisa McKendall, insisted that any erotic allusions were unintentional. “We’re not in the business of putting cock rings into the hands of little girls,” she said in an interview at the time. “We asked girls if Barbie should get a new boyfriend or stick with Ken. They wanted Barbie to stay with Ken, but wanted Ken to look a little cooler.”

There might not yet be a gay or trans Barbie, but her look has certainly diversified over the years, from her wasp-waisted, porcelain-white skin beginnings. A revealing lineup of dolls shows how facial features and body types have evolved, from the first black doll, Christie, in 1968, to the influence of Barbie’s English friend, Stacey, released the same year – whose head mould then became used for Barbie in the following decades, as her mod fashions, swinging London house interiors and Austin-Healey car also nodded to English cool across the pond. But it wasn’t until 2016 that Barbie’s body became (slightly) more realistic, with the release of “petite, tall and curvy” versions, launched with the tagline: “Imagination comes in all shapes and sizes”. 2022 saw the range expand further still, with prosthetic limbs, hearing aids, and wheelchairs, while last year saw the first Down’s syndrome Barbie, designed in collaboration with a US charity.

“You can’t say Barbie is radical,” says Thom. “It’s a mass-produced, corporate product. But there is an element of progressivism to it.”

She highlights the black female president Barbie, released back in 1992, and the Miss Astronaut Barbie launched in 1965 – four years before the first man stepped on the moon. In the 1980s, Barbie was already conquering boardrooms, working as a doctor, vet, army officer and Olympic athlete, while more recent sets have ranged from Eco Leadership teams (including renewable energy engineer and chief sustainability officer) to political campaigning dolls – featuring a placard-waving activist Barbie. All of these iterations are shown in vitrines designed by Sam Jacob Studio, whose candy colour palette and inventive touches throughout the exhibition (including a surreal chandelier made of dolls’ hair) create a perfectly tuned backdrop.

So what next for Barbie’s style? The most recent Dreamhouse on show, from 2021, shows a clear return to her modernist roots, drawing on California Case Study houses, only rendered in a searing colour palette for the Instagram age, complete with selfie-friendly yellow swing chair and wavy pink slide – and a phone-holder in her karaoke penthouse. There are no twiddly mouldings in sight.

But, as the world takes a reactionary turn once again, with a possible second Trump presidency threatening to enforce classical federal architecture laws, and even Britain’s Labour party keen to usher in Neo-Georgian new towns, might we see Barbie follow suit and ditch her plastic penthouse for something more trad? Perhaps a nostalgic Poppins Barbie Edwardian terrace house, with a spare bed for cautious Ken Starmer, awaits?

• Barbie^®: The Exhibition is at the Design Museum, London, from 5 July to 23 February.