After six years in the Sugarcubes and 15 years of solo work, Björk Guðmundsdóttir (to give her her full name) still remains something of an enigma to those who follow her career.

She's been a singer, an actress, a composer and a producer. She's worked with beat-boxers, Inuit choirs and well-known eccentrics. Her music has veered from punk, to jazz fusion, to lush orchestral sweeps, to bludgeoningly heavy beats.

The 42 year-old comes to Sheffield as part of a massive tour to promote her sixth studio album Volta. A mere mention of who she chose to work with on the record tells a lot about the woman's enigmatic eclecticism. Few albums will hear the tortured wails of Antony and the Johnsons singer Antony Hegarty and the sharp, modernist beats of renowned hip-hop producer Timbaland sitting comfortably alongside each other, with Björk's trademark shrieks and coos working their way around the middle.

Björk's first proper solo album (if you ignore her album Björk which she recorded at the age of 11) was a massive critical success; Debut was named NME's album of the year for 1993, and she picked up two Brit Awards in 1994 to prove it. However, it was the 1995 release of It's Oh So Quiet – a renamed cover of Betty Hutton's Blow a Fuse – that really introduced Björk to the nation. Her eccentric performance, the track's big-band styling and the joyously day-glo video meant that few people were unaware of the pixie-ish singer. The song stayed in the UK top 40 for 15 weeks. Björk has since disowned the song that her label, One Little Indian, released in the hope it would achieve success in the novelty Christmas single market.

However, it was the next year that Björk cemented herself in the public's consciousness. First, having been confronted by a mob of reporters and photographers when she left a Thai airport with her ten year-old son, she attacked one reporter. Later that year an obsessive fan posted an acid bomb to Björk's London home before filming his own suicide. Fortunately, the package was intercepted by police. Björk's avoided commenting on the incidents, but has publicly apologised to the reporter.

Her personal troubles hardly made Björk meek or desperate to shrink away from the limelight. Proof of her continuing eccentricity can be easily found in her choice of outfits. Her notorious "swan dress" worn to the 2001 Oscars may have surprised some, but even that paled in comparison to the frock she donned while performing at the opening ceremony for the 2004 Summer Olympics in Athens. While singing Oceania, a song written for the occasion, performed alongside Leeds-based beat-boxer Shlomo, Björk's dress unfurled into
a 900 square metre map of the world which flowed over the gathered Olympic athletes. How's that for flamboyant?

Implausibly enough, Björk's film career could actually make her musical output and dress sense seem somewhat anodyne. Her most famous film role as the lead in Lars von Trier's 2000 film Dancer in the Dark was a great success and won Björk the Best Actress Award at the 2000 Cannes Film Festival. Dancer in the Dark was more devastating than shocking, however, and it was one of Björk's more recent forays into acting which saw her doing something somewhat more outlandish.

The 2005 film Drawing Restraint 9 saw Björk collaborating with her partner, filmmaker Matthew Barney. With Barney directing, Björk created the soundtrack and the couple also took the film's lead roles. It was an almost dialogue-less two-hour exploration of Japanese culture set on a whaling ship. The film comes to a stomach-churning climax when Björk and Barney, swimming in a pool of sea-water and vaseline, cut off each other's limbs, eating the flesh as they go, gradually transforming themselves into primitive whale/human hybrids. More recently, Björk caused political controversy by dedicating her single Declare Independence to states and nations she believes are being unlawfully occupied. Dedications have gone to Greenland, the Faroe Islands and the Aboriginal people of Australia. More divisive were her cries of "Kosovo! Kosovo!" while performing in Japan – which seems to have lead to her withdrawal from Serbia's Exit festival – and her shouts of "Tibet! Tibert!" during a concert in Shanghai. Björk's outburst in Shanghai led some to believe that the Chinese government might make it harder for foreign musicians to perform in China, although this worry seems to be unfounded. Chinese authorities did however block access to Björk's official website.

Björk later made a statement, but did not apologise or back down: "I am not a politician," she wrote on her website. "I am first and last a musician and as such I feel my duty to try to express the whole range of human emotions. The urge for declaring independence is just one of them, but an important one that we all feel at some times in our lives.

"This song was written more with the personal in mind but the fact that it has translated to its broadest meaning, the struggle of a suppressed nation, gives me much pleasure. I would like to wish all individuals and nations good luck in their battle for independence."

What can we expect in Sheffield? A cry for Yorkshire independence? You almost wouldn't put it past her, would you?

Björk plays Sheffield City Hall on May 4. Box office 0114 278 9789.