She's reinvented herself many times since starting out with Icelandic pop-punks, The Sugarcubes. But Bjork's recent forays into politics have made some wonder is she developing a Bono complex? And should her Belfast audience be anticipating any words of wisdom on the peace process?
When Bjork took the stage last month in Shanghai, and, as she put it, 'whispered' the word Tibet repeatedly into the microphone during the performance of her song, Declare Independence, the whisper soon became a roar that was heard around the world, not least by the Chinese government in Beijing.
Although Bjork quickly pointed out that no-one at the concert complained about her efforts to draw attention to the suffering of the Tibetan people at the hands of China, the Ministry of Culture said Bjork had "deliberately turned a commercial show into a political performance, which not only broke Chinese law, but also hurt Chinese audiences' feelings".
For Bjork, who released her first record at age 12, the incident marked yet another stage of growing up in public. The Icelandic singer had previously insisted that all her lyrics were intended to be personal, and that she wanted to have nothing to do with 'party politics,' but in this case she was forced to defend herself.
While saying that the song Declare Independence was written as a personal statement, she admitted that it could apply to political situations like that of Tibet — "the struggle of a suppressed nation".
Of the upcoming Olympics, Bjork further was quoted as saying: "I think having thousands of visitors who are used to freedom of speech will be a big challenge for China."
In fact, prior to the Chinese controversy, while on stage in Japan, she had already dedicated the song to Kosovo, which had just declared independence from Serbia. As a result, a Serbian concert she was due to play this summer — the internationally famous and critically respected Exit festival — was swiftly cancelled.
Her outspokenness on the Tibet issue has moved some to comment that Bjork has soured her chances of singing at this year's Olympics. At the opening of the 2004 Olympics in Athens, she memorably performed the song Oceania while the fabric of her dress, on which a map of the world was depicted, extended across the whole arena, forming a sea-like expanse in the amphitheatre.
It was a stunning moment: visually arresting, unusually intimate, and an undeniable moment of calm during the feverish Olympian proceedings. Such broad and imaginative strokes have been characteristic of a career which has brought a rare artistry to the making of pop music.
Bjork came to prominence in the late 1980s with the Icelandic band The Sugarcubes, a collective of avant-garde pranksters from Reykjavik who were as surprised as anyone when their single Birthday became a hit in the UK charts after the late John Peel championed it.
"It was a hobby really," Bjork told an interviewer in 1995. "We'd all get drunk at weekends and write these weirdo pop songs and then when we had enough we could go on holidays as The Sugarcubes. It was just a group of friends travelling all over the world and thinking: 'This is crazy'!"
After The Sugarcubes disbanded in 1992, Bjork recorded the album Debut with Nellee Hooper, who had produced Massive Attack's classic album, Blue Lines. This was the first sign of what would become a habit of Bjork's: cannily choosing collaborators to fit her conception of her latest record.
Bjork's solo career has seen her collaborate with Icelandic choirs, throat-singers and hip-hop beatboxers on 2004's Medulla (a record made up primarily of vocals and vocal samples).
She has also tracked down the finest dance producers to help her transfer "the songs I'd written in my head" to tape — she recently worked with hip-hop producer Timbaland, and has frequently recorded with Mark Bell of London techno group LFO as producer.
Her most recent album, 2007's Volta, saw her duet with Antony Hegarty, of Antony and the Johnsons, and utilise the expertise of Malian kora player Toumani Diabate.
What Bjork has preserved throughout her solo recording career is a strong melodic sensibility that shines through even her most experimental compositions, and a commitment to producing the best work possible. "Mediocrity has never been my strong point," she once said.
Where some artists might keep their finest songs for their own albums early in their career, Bjork's song Play Dead, her contribution to the soundtrack for the 1993 film The Young Americans remains one of her best tunes.
There has been a dark side to Bjork's career too. In 1996, after arriving on a long-haul flight to Bangkok airport, Bjork attacked a journalist, garnering her even more tabloid attention.
That same year, an obsessed fan sent Bjork a letter bomb, killing himself after it was sent. The package was intercepted by police, and Bjork still refuses to talk about the events. The repercussions were obvious, though: Bjork was now headline news.
An invitation from Danish director Lars Von Trier saw Bjork star in the musical film Dancer in the Dark, released in 2000.
At that year's Cannes Film Festival Von Trier's film was awarded the Palme d'Or, and Bjork was proclaimed best actress.
Bjork's work on the movie soundtrack, released on CD as Selmasongs, was recognised when she was nominated for an Oscar for best song.
Famously, on the way in to the auditorium before the awards ceremony, the swan dress Bjork was wearing laid an egg on the red carpet.
But Bjork's experience on set with the notoriously volatile Von Trier put her off acting, seemingly for good.
In interviews she said that she would never act in film again, that the making of Dancer in the Dark had been too "emotionally taxing", and that she preferred instead to concentrate on music.
Subsequently, Bjork moved to New York, and began a long-term relationship with American artist and filmmaker Matthew Barney. In 2002, the couple had a daughter, and in 2005, Bjork composed the music for, and acted in, Barney's film Rawing Restraint 9.
During this time, Bjork has increasingly been credited as the sole producer on her records.
She has acknowledged that she has become more interested in current affairs as a result of events such as the Iraq conflict and the Indian Ocean tsunami of 2004.
The controversy around Declare Independence suggests that she has found a way to link her personal concerns to the wider world.
Whether this controversy is something she will want to repeat remains to be seen: Bjork is someone who enjoys performing, but instinctively dislikes the celebrity baggage it brings.
Politics are one thing, but you get the feeling that, for Bjork, the music is the most important thing of all.
Bjork plays the Waterfront Hall on April 28. Box office 9033 4455.