Kwon Ji-yong aka G-Dragon wearing shoes from his collaboration with Giuseppe Zanotti.

The thick end of this cultural wedge, the most visible, audible and obvious part, has been the music and the fashions that come with it. K-pop stars have swept the charts in Hong Kong and the mainland, and broken through to the West, fronting a so-called Korean wave or Hallyu (a term coined by the Chinese press) in Europe and North America. Korean designers are making a splash, too, in the traditional fashion capitals, with the Concept Korea show at the recent New York Fashion Week garnering a lot of attention for designers Lie Sang-bong, Lee Suk-tae and Lee Ji-yeon.

What began with K-pop moved on to a global obsession with Korean television and film. A fad quickly became a trend and then a movement. Korean superstars such as Kim Soo-hyun, star of the hit show My Love from the Star, stare down from giant billboards advertising everything from cars to mobile phones in Hong Kong, Singapore, Shanghai and Tokyo. Inevitably, then came the fashion. Fans were keen to dress like their Korean idols.

See also: Hot looks this week: K-pop fashions

"Hallyu is indefinable without fashion," says singer Jiyul, of K-pop girl band Dal Shabet. "Fashion has influenced K-pop in many ways, allowing celebrities, like myself, to look their best when performing on stage. K-pop would not be where it is today without fashion."

Western brands have seen the enormous influence of stars such as Jiyul, with sales spiking on single Instagram pictures or mentions on social media. Many have formalised the link and collaborated on special collections. Italian shoemaker Giuseppe Zanotti, for example, has linked up with G-Dragon, named one of the 500 most influential people in fashion globally by Business of Fashion magazine, to create a line of loafers.

Cindy Yun, chief executive of Atria Style.

This intertwining of fashion, music, film and television has allowed Seoul to become arguably the most fashionable and culturally influential city in Asia, taking the unofficial title from long-time holder Tokyo. In terms of online sales, e-tailer matchesfashion.comsays Seoul has just taken over Hong Kong as its biggest Asian market and third biggest market worldwide.

Chanel, under Karl Lagerfeld, presented more tangible evidence for this shift to Seoul in May, when it unveiled its 2016 cruise collection in the South Korean capital. The next meeting of the prestigious Condé Nast International Luxury Conference will be held in the city in April.

So Seoul is cool, and Korean fashion is enjoying its moment in the sun, but what is K-fashion?

"I don't really understand what it is, or why people see what I do as 'Korean'," says Kang Dong-jun, also known as Kang D, the designer behind conceptual label D.Gnak and diffusion line D by D. "Some people say it's a tailoring style that's particularly Korean, but I'm not sure at all."

Beyond focusing on a darker colour palette and being incredibly well-made, the label does defy definition. For instance, Kang's latest D by D collection (available at Harvey Nichols) comprises mixed fabrication activewear inspired by a trip to Mongolia. Moreover, a great number of the nation's leading designers studied fashion outside Korea, steeping themselves in an international approach to their trade. Kang D attended New York's Parsons School of Design, although he admits he didn't particularly enjoy the experience, his time in the city coinciding with the 9/11 attacks.

Veteran designer Lie's aesthetic is markedly different to that of Kang D. Favouring colour, patterns and lashings of eccentricity, Lie's most recent collection, presented in New York, incorporated hangul (Korean characters) into his clothing, linking his culture with contemporary fashion. Lee Suk-tae, who studied in Paris and worked at Christian Dior and Sonia Rykiel before founding his own label, Kaal E Suktae, favours structured and avant-garde designs.

Seoul's influence on local fashion is clear at Aland, the Korean multi-brand fashion store with a big Causeway Bay flagship. Young fashionistas fill the shop, rifling through the affordable kitsch accessories and quirky, athletic-chic fashions. One of the first companies to expand overseas, Aland has opened three stores in Hong Kong in less than two years.

The Atria Style store in Hongdae, Seoul.

"K-fashion used to be seen as the cheaper version of the Japanese style," says Cindy Yun, speculatively, before emphasising that defining K-fashion misses the point. The founder and chief executive of fashion retail and technology company Atria Style, which has just launched in Hong Kong, in collaboration with I.T, Yun has quickly become a kingmaker in Korean fashion. Her company retails the work of some of the country's best and brightest fashion talent but also helps package and present it to the world.

"When you think of Korean fashion, people actually have a hard time defining it. If I asked the average person to name some Korean brands, they might not know any," says Yun. "That's where Atria Style comes in. We have over 200 designer brands, brands with international appeal and ready to sell abroad, but everything is made in Korea."

The daughter of a former Miss Korea, Yun cuts an impressive figure, wearing the accoutrements of wealth one would associate with the Gangnam district of Seoul. Within minutes it becomes apparent that she's a canny operator keener on the mechanics of fashion and exploiting a trend to the fullest than the glamour of the business.

"We're actually behind a lot of Korean celebrity styling," says Yun, who is on her fifth business start-up in 15 years since graduating from New York's Fashion Institute of Technology with a degree in fashion merchandising. "We work closely with Korean celebrities from the popular dramas and K-pop. Basically, we dress them with Korean designer brands. So we're not only the retail platform, we're like a content provider as well."

Yun then reels off ways in which her company is able to leverage the star power of Korean celebrities, merging content creation with business by creating apps that allow consumers to watch a drama and, with one tap of the tablet or smart TV screen, find out immediately what the stars are wearing and how to buy the items.

People such as Yun are reshaping the Korean fashion industry to better compete abroad, fixing supply-chain issues for smaller brands and establishing what she calls a "designer fast fashion" culture.

Kaal E Suktae's autumn-winter 2015 runway show at Seoul Fashion Week, in March.

"Usually, designer brands produce spring-summer and then autumn-winter [collections], they work over a six-month period and production takes around five to six months. For the designs to actually come out takes about six months to a year. But for Korean designer fast fashion, production lead time is less than 30 days," says Yun, adding that she admires the success of fast-fashion behemoths Zara, H&M and Uniqlo but believes they lack identity.

Atria Style is all about maximising the trend as quickly as possible, says Yun, and her view is that putting "designer identity branding onto the fast-fashion production" stacks up with all the data she has on consumer behaviour. That is, people want what they see, they want it fast and they want it at a reasonable price.

" Hallyu and fashion, hand in hand, contribute to the Korean economy and provide opportunities for those outside Korea to know the country and culture better," says Jiyul.

With all this potential for global growth, fashion giants such as LVMH, the world's biggest luxury goods conglomerate, see the upside of direct investment into Korean pop culture. Last year, L Capital Asia, an LVMH investment vehicle, made an US$80 million investment in YG Entertainment, one of the top three music companies in South Korea and home to Psy and G-Dragon. The deal is mutually beneficial, LVMH getting direct access to a roster of stars who have pan-Asian appeal and loyal and highly suggestible fan bases and YG being given another revenue stream for its stars to add to a recent expansion into beauty products.

Looks from Kang Dong-jun's diffusion line D by D.This marriage of creativity and commerce is underpinned by a level of government support that provides another stark and embarrassing counterpoint to the approach favoured in Hong Kong. As well as backing the Concept Korea showcase at New York Fashion Week, the Korean Ministry of Culture, Sports and Tourism and the Korea Creative Content Agency have been helping fashion designers and creatives to break into overseas markets with mentorship, education and legal and administrative support. In Hong Kong, the Korean consulate has run an annual event to showcase the country's best talent and produce. Now in its fifth year, Festive Korea, which runs throughout October, gives a platform to up-and-coming designers such as Woo Cho, who held his fashion-show debut at PMQ this month.

After recognising the current K-wave, one has to consider whether there will be a K-crash; remember when all of Asia looked to Japan for fashion cues? And it isn't entirely unreasonable to expect China to eventually dictate taste in the region.

"It's hard to predict a definite month or year when this trend will finish, or if it ever will," says Yun.

Her goal is to create a self-sustaining fashion ecosystem that can survive the quirks of trends but, for now, she's bullishly optimistic.

"The market is actually unlimited at this point and we have [only just] launched here!"

3 Korean fashion labels to look out for

Beyond Closet The ultra-hip menswear label is the brainchild of designer Ko Tae-yong, whose fondness for all things American is combined with tight classical tailoring and flashes of wit and personality. Ko often mixes preppy staples such as Oxford shirts and stripy jumpers with puppy-dog logos and motifs.

Pushbutton A long-time darling of the critics, Pushbutton is famed for its quirky approach to fashion and is an accurate reflection of creative director Park Seung-gun, a fashion-school dropout, former K-pop singer and model. Park enjoys playing with people's expectations and loves colour.

Kye Kathleen Kye is one of the designers who garnered global critical acclaim through the Concept Korea platform at New York Fashion Week. A graduate of London's Central Saint Martins, Kye was trained in menswear. She now focuses on womenswear but retains a penchant for strong masculine silhouettes.