London-based Hadid is at the top of a profession that's notoriously difficult for women to enter, let alone conquer. Her designs, once dismissed as brilliant but impossible to build, are now springing up around the globe, with projects such as the Guangzhou Opera House due to be completed this month and the Aquatic Stadium for the London Olympics nearing construction stage.

The flamboyantly dressed Hadid, who has a penchant for designers Yohji Yamamoto, Issey Miyake, high heels and weird coats, and who streaks her tousled hair blonde on top and pink underneath, has succeeded through sheer force of personality. She is energetic and has a reputation for being volatile - vital traits for crashing the elite men's club of British architecture.

Now 57, Iraqi-born Hadid came to London from Beirut in the early 1970s to study architecture. 'Perhaps it was my flamboyance rather than my gender that made me determined to succeed,' she says, 'but I've always been determined - it's been a long struggle'. Now she's finally doing what she's always wanted to do: dreaming up buildings unlike anything we've seen and having them built.

The current exhibition at London's Design Museum illustrates the breadth of her projects that include the BMW building in Leipzig, a ski jump in Austria, a science centre in Germany that resembles a space ship, museums and galleries in Rome and Calgary, an arts centre in Abu Dhabi, and the Contemporary Art Centre in Cincinnati (the 1997-2003 project that cemented her reputation).

The boulder-shaped opera house in Guangzhou is her latest achievement - and a very different one at that. 'In China, certain analogical thinking makes more sense to people than in the west.

'The idea of pebbles and rocks in a stream for the opera house design is actually meaningful to them. For us, the idea was more of a technique to articulate the relationship of landscape and building.'

Using the landscape is how Hadid brings the form and function of a building together. 'When I was in Beijing for the first time, people asked me, 'How long did it take you to build Cincinnati?' They were surprised when I said two years. They felt it was too long and said in two years they would have built seven towers. The pace of construction is much faster in China than Europe or America.'

Today software technology makes it easy to construct one of Hadid's flowing undulating forms, but in her early days it took special engineering expertise to realise the extreme geometry of her projects. There are few straight lines in her work; her futuristic buildings give the impression of waves, gently curving shapes moving in unexpected directions with the occasional jagged edges. A key element is the layering of the different levels; looking at the function of the building and how the public will use it is integral to her work. She likes to construct buildings that create an original experience, a sense of wonder: 'continuing to arouse curiosity is a constant theme in our work', she says.

Her first major commission was to design The Peak flats complex and nightclub in Hong Kong in 1982, which marked the transition from experimental ideas to architectural concept. The plan was for dramatic, gravity-defying jagged splinters stuck in rock, designs that would sit comfortably in a George Lucas film. 'I wanted to inject a new level of dynamism into architecture, so for The Peak we metaphorically flipped the Hong Kong towers to create a horizontal cluster of beams.'

Although the plans were scrapped as a result of the Asian stock market crashes in 1984, the architectural language she employed shaped the thinking of subsequent buildings such as the BMW plant in Leipzig and the Museum of 20th-century Arts in Rome.

'It was a seminal project for us,' says Hadid, 'but I don't think it would make sense to build the unrealised design now. If I were to do it again, it would have to be an interpretation of what might have been as my work has developed, and so has Hong Kong. The Peak project tested our ideas on landscape topography and you can now see the results of this in all our work'.

Hadid's early work was considered radical and unworkable so she spent 13 years in the wilderness before designing a fire station in Germany in 1993. Her ideas often grated with others, but it was her determination that saw her overcome hurdles, and in 2004 she won the Pritzker, considered the world's premier architecture prize.

The award opened doors for her and since then she has designed the Aqua table, a Louis Vuitton bag and Chanel's nomadic exhibition venue which will feature an etched quilted fibreglass exterior and a spiralling sea-shell interior. It is what you would imagine a luxury spaceship to look like. Thrilled with the results, Lagerfeld says of Hadid: 'This woman is pure genius. At the same time she's tough and fun.'

Hadid, who will be in Hong Kong for the opening of the Chanel exhibition, says: 'I'm intrigued with the urban interventions of the old guard Modernists such as Corbusier and the Corbusian model is still very strong in Hong Kong.' 'It is spectacular because it works on so many levels: with layering of transport, retail, commercial and residential blocks in porous, mixed-use developments - no other city is so integrated in its architecture and planning.'

Recalling her early childhood in Iraq, Hadid says she was inspired by the landscape of the Marshes in the south of the country.

'There was this flow between the sand, the water and the wildlife that incorporated the buildings and the people.

'What I'm trying to do as an architect is capture that seamless flow in an urban context.'

It goes some way to explain Hadid's original vision, which makes her one of the most exciting modern architects. 'Through architecture we give people a glimpse of another world,' she says.