In one corner of the exhibition, Waist Down: Skirts by Miuccia Prada – shown in Rem Koolhaas's radical new "Transformer" building in Seoul – there is a row of skirts swinging from side to side as if dancing. Across the cocoon-like space, others are variously whirling, fluttering or billowing like Marilyn Monroe's famous white dress. Of course they are moving mechanically, but the illusion that they have a life of their own seems appropriate for designs with such a strong identity. Since Miuccia Prada became the creative director of Prada, the skirt has been the canvas for some of her most imaginative designs and this exhibition shows a diverse collection from 1988 to the current season. It's also fitting that an exhibition which celebrates movement, change and experimentation should be shown in a structure which can be reconfigured into a new shape. Unveiled last month, the space-age, tetrahedron-shaped Transformer, made from an elastic membrane stretched over a steel frame and situated near the traditional Gyeonghui Palace in Seoul, will change shape to host film and art exhibitions after Waist Down.

"I like skirts because they enable me to wear something eccentric without it looking too complicated or being a big deal," explains Miuccia Prada, at a party to celebrate the opening of the Transformer. The designer herself embodies this philosophy perfectly, frequently teaming an intricate skirt, such as a lime-green box pleat or feathered design, with a crisp white shirt or plain wool top. She added that Waist Down was the perfect

complement to the Transformer as it "explains the Prada process, as well as being the only exhibition we have done about our work." Or as curator Kayoko Ota phrases it, "the skirt is a message from Mrs Prada to the wearer".

Every season, that message is one of fashion's most eagerly awaited; the Prada skirt is one of the most influential garments of the past 20 years. Miuccia Prada is seen as something of an oracle in the industry, and where she boldly goes with her designs, many other labels, and then the high street, dutifully follow. However, Prada's brand of radicalism is not about creating overtly conceptual clothes in which function is a poor relation to form, rather it is about confounding expectations and subtly surprising the audience with an unconventional beauty. Her autumn/winter 2007 collection showed knee-length skirts made from tufty, teddy-bear-like alpaca wool, and techno fabrics crinkled to look like bark.

In an era where so much design looks to the past, this was a genuinely original collection with little attention paid to conventional notions about flattering the figure; Prada has said that she actively disregards the idea of creating clothes that make the wearer look slim. In fact this jolie laide quality, the wilful embrace of fabrics and shapes that can appear perverse on first look, intriguing on the second and strangely seductive thereafter, defines much of the label's thoughtful aesthetic. The following collection, for spring/summer 2008, took a dreamy departure courtesy of enchanted Arthur Rackham-style fairy prints on billowing silk, calf-length skirts, and then, entirely unpredictably, the following show for autumn/ winter 2008 showed a more direct, brooding sexuality in the form of pencil skirts made from hand-worked Swiss lace.

Examples from these collections – including a lime-green skirt with a sinuous illustration of plants and fairies, an ink-coloured lace skirt with a short peplum, and a tufted wool skirt with a primitive quality – appear in the exhibition alongside other memorable pieces. There is the Formica-print skirt which recalls Fifties home furnishings, from the autumn/winter 1996 collection. When it appeared, it offered a dramatically different and less overtly sexual alternative to the sultry rock groupie-look velvet flares offered up by Tom Ford, newly installed as the creative director at Gucci. Among the most appealing prints are the lips and lipstick patterned skirts from spring/summer 2000, which recall the eroticism of vintage Yves Saint Laurent.

Viewed together, the collection offers not only an insight into Prada's oeuvre, but an instructive lesson in how to buy clothes that last. All the skirts could be worn this season without looking dated, because they reflect the designer's own tastes rather than a particular season's trends, but the ones which look the most relevant today are those that make the boldest statement. The real investment clothes aren't safe classics, but unusual, special clothes that amount to wearable pieces of art.

Miuccia Prada is an avid art collector and supporter, but up until now she has been hesitant to explicitly combine clothes and culture. Waist Down has previously been shown in the Herzog and de Meuron-designed "Epicentre" store in Tokyo, the Peace Hotel in Shanghai and the New York and Beverly Hills Epicentres, but this is the first time it has been in a dedicated art space. As Tomaso Galli, communications director of Prada explains, the business has been "very active in the world of culture and art, but for Mrs Prada it has been key to keep it separate from fashion, until now when we felt we wanted to pull art, architecture, film and fashion together in Asia, in a very Prada way. In a very unique and unexpected way." Miuccia Prada explains that the Transformer was "the result of a long discussion. I never wanted to put art and fashion together, but working with Mr Koolhaas made me change my mind, and I liked the idea of doing this project in another country."

Numerous Western fashion companies have worked on projects in China, but Prada and Galli felt that South Korea was a more original, not to mention culturally exciting place, to stage the exhibition. The fashion scene is a dynamic one, with design courses at many universities, and this version of the exhibition features skirts by eight Seoul fashion students who were asked to reflect on traditional Korean aesthetics while exploring the capacity of a skirt. One of the most striking was a fan-pleated skirt by Myoung-Shin Lee which was influenced by both traditional packaging and the line of the Gyeonghui Palace roof. In a time when most companies are tightening their belts, a 180-ton, 20-metre-high art space with more than a passing resemblance to a UFO might seem somewhat counterintuitive, but Mrs Prada seems unfazed. "We are in exciting times," she shrugs. "[The recession] might bring some changes, but any changes are a source of newness, and I like newness."