Matthew Barney: Mr Björk comes to town for his new London exhibition

Matthew Barney only turned 40 this year, but has already been hailed by the New York Times art critic Michael Kimmelman as "the most important American artist of his generation". Whether he is working with film, sculpture, photography, drawing or performance art, Barney has an uncanny ability to create images that linger in the memory banks. He is best-known for his film series, The Cremaster Cycle, and the Serpentine museum in London is now preparing to host an exhibition revolving around Barney's last film, Drawing Restraint 9, which sees the New-York-based artist look east, to Japan, for inspiration. Barney appears in the film alongside his partner, and the mother of his child, Björk.

There is no hiding from the fact that Barney's films are nigh on impossible to understand to all but a handful of people. Handily for The Cremaster Cycle, there was a tome seemingly designed with weightlifting sessions in mind to help understand some of the intricacies of Celtic mythology, the Freemasons, the colours of American football kit and testicular physiology. Barney is a former athlete and model, which goes some way to explaining why sporting motifs and perfect human bodies always crop up in his oeuvre.

The exhibition arrives in the UK with an invaluable documentary, Matthew Barney: No Restraint being released simultaneously on DVD. In this, Alison Chernick helpfully asks all the questions that you were too embarrassed to ask. It is Björk, in her unique English, who gives the best interpretation of his work and, in doing so, gives a very brief insight into why their marriage seems to work. "He is a sculptor and this work grows and becomes all these other thing that are being done to serve his sculptures... [the work has] so many layers and attempts to make us drop our desire to use the analytical mind."

His sculptures, drawings and installations relating to the film, which will be paraded in the gallery under the headings Drawing Restraint 1 – 15, sell for big bucks through the Barbara Gladstone gallery in New York, which housed a version of the exhibition last year. There will also be a first chance to see Drawing Restraint 9 at UK cinemas as it finally receives a limited release at the end of September, to coincide with the exhibition. All of which means that the acclaimed American artist will be difficult to avoid over the next few weeks.

The film from which all the other works in the Drawing Restraint project derive is about a Western couple (played by Barney and Björk themselves) who fall in love over cups of tea served by the rules of a traditional Japanese tea ceremony. The couple are on board the notorious Nisshin Maru, the only factory whaling ship currently in operation in the world.

Barney only started to work on the project in earnest once the Cremaster Cycle was completed in 2004, and when he finally received permission from the Nisshin Maru to shoot on the ship. He reveals that the owners of the Nisshin Maru, which has been the focus of several Greenpeace anti-whaling campaigns were understandably concerned with his plan to shoot a film on the ship; "It's is an environmental icon so they were very nervous to get involved in something like this, and it took the better part of a year to convince them that the project had a neutral political position."

The position on whaling in the film is a reflection of his own views. "The more you look into the subject the more it starts to be a little more complicated than the negative view in the West of Japanese whaling. I wasn't interested in taking on a political standpoint, but I was very interested in making a story that happened within a politically charged piece of architecture.

"The film starts with a letter I found that was written by a Japanese woman to General MacArthur during the American occupation. There was, at a certain point, a lot of praise for General MacArthur for bringing democracy. One of the things that I found interesting for this story was that MacArthur had suggested to Japan that the whaling moratorium be dropped for them, and that they take their surviving military ships and start factory whaling to feed the nation." Clouding the muddy waters even further is the fact that when the exhibition opened in New York and San Francisco, Barney appeared dressed as MacArthur.

After his parents divorced, Barney lived in Idaho with his father. His mother moved to New York, and it was on visits to the Big Apple that his fascination with art was cultivated. After graduating from Yale in 1991, Barney entered the art world and garnered instant success. In 1996 he won the Europa 2000 prize at the Venice Biennale. He met Björk in 2000 when she was in New York, promoting her star turn in Lars von Trier's Dancer in the Dark. Their baby daughter Isadora was born in London, where Björk had set up home in 2002.

It has often been rumoured that the couple have split, as they spend so much time apart, Björk has once again set up base in Reykjavik and Barney has a home in New York City. Officially they share a home in Palisades in New York State. After six years together Barney thought Drawing Restraint 9 was the right project to finally work with his partner, saying: "I believed that working with Björk would make it easier to show the love story, but there was also the interest for both of us that the subject matter of the film was about our [humans] relation to nature." A handy by-product was that Björk created an atmospheric two-and-a-half-hour soundtrack.

Barney is noted for being introspective and not a good talker. He takes his time when he is speaking, mulling over every response. He has a fine physique, developed while playing American football for his high school in Idaho. Some of his most fervent critics have used his good looks and pop-star wife as proof that the artist is style more than substance, but this ignores the talent which is undoubtedly at work. Barney uses his experience of training for sport to feed into both his work and creative process. He says, "I grew up as an athlete, and I started thinking about the notion that the muscles and cells in your body are dependent on resistance in order to grow and how it might be useful to think about productivity and creativity in the same way and that it too might have a relationship to resistance, might rely upon resistance and be useful in the sense that one's cycle of creativity takes you to places where you feel lost." He quips: "Another obtuse answer."

Barney is unduly worried about his performance as a speaker. In person he is always crystal clear when talking about his work, making me wish that he would produce a DVD-style commentary to accompany it. He also admits that the success of his films away from the art exhibits came as a surprise. "I didn't start with the ambition of showing my films separate from the exhibits. It sort of happened organically and now that I can see it exists in both places it makes my desire for the piece to operate more coherently as a narrative film stronger. The other criteria for the films are to be fertile text that I can draw from to make objects."

'Matthew Barney: No Restraint' is released on DVD on 24 September. 'Drawing Restraint 9' will be on limited release from 28 September. Matthew Barney, Serpentine Gallery, 20 September to 11 November