In a short hallway, somewhere inside the labyrinthine Basel HQ of Herzog & de Meuron, stands a small Chinese wooden table, shaped so that two of its legs rest on the floor and two on the wall. It's an artwork by Ai Weiwei, a friend of the Swiss architects and a regular collaborator. Above it hangs a giant light fitting, designed for their most famous collaboration: Beijing's Bird's Nest Olympic stadium. This "shrine to Weiwei", as the architects put it, says plenty about their practice: few architects have cultivated such close ties to artists and the art world in general, or benefited from them so handsomely.  In room after room of their vast studio, members of their 350-strong team labour on new art galleries and cultural buildings. Here's one for Miami: an open concrete structure with an oversailing roof. Over there is a huge art gallery in Kolkata; elsewhere, there are buildings in New York, Hong Kong and São Paolo. Meanwhile, on an island in Hamburg, their stunning Elbphilharmonie concert hall has just had its topping-out ceremony.  And this summer the architects will be revisiting London, home of their Tate Modern. In July, we'll see the first signs of their long-delayed extension to the gallery: a conversion of the old power station's subterranean oil tanks. But before that, they'll unveil the 12th in the Serpentine Gallery's series of temporary summer pavilions, another collaboration with Ai.  Just as Basel is an art hub, so too is it home to pharmaceutical giants, who have regularly employed their local super-duo. In fact, the whole city is strewn with the architects' early works, from industrial buildings to high-rise office towers to the local football stadium (plus, of course, galleries and museums). Not that you'd instantly recognise their work: what's facilitated Herzog and De Meuron's ascent has been their capacity to re-think architecture anew. Their nearby Central Signal Box, from 1999, wrapped a bog-standard piece of railway infrastructure in twisting bands of copper to create a sculptural landmark.  "I think we are the largest experimental practice in the world," says Jacques Herzog. The two have been friends since they were six, through school, university, setting up together in 1978, and collecting a joint Pritzker prize in 2001. They have been compared to Gilbert and George (though they are both married with children) and even Star Wars's C-3PO and R2-D2. Pierre de Meuron (rounder features, more hair) is the more retiring one and Jacques (thinner) the talker, and so it proves when we meet.  "Architecture is always an expression of some transformation in our culture," says Herzog of their art-related workload. "There is too much gallery space in the world. Private collections have grown tremendously, the size of artworks has grown, art prices are too high. The problem is that public institutions cannot buy art any more. Is this a bubble? Perhaps, yes. I don't care so much. Institutions which don't work and don't make sense will disappear with the same speed they've come in. They will be turned into restaurants and office buildings."  It is usually Frank Gehry's Bilbao Guggenheim that gets cited as an example of city-changing architecture; their Tate Modern has, arguably, been equally significant. London was already on the cultural map, but Tate Modern's colossal success altered its centre of gravity in a way few other buildings have – and created a new type of public space with the cavernous Turbine Hall. In turn, the hall has inspired a new breed of macro public art, including Ai's memorable Sunflower Seeds installation. What's more, in contrast to the Guggenheim, it did all this not by building something new and attention-grabbing but by transforming what was already there.  Herzog describes Tate Modern as "the key project in our career". "It was the real jump to the largest possible exposure you could have anywhere, because nowhere else would you attract as many people – twice as many as in New York. It trained us, helped us understand what architecture can do: to be more than just fulfilling the brief and giving the physical structure, but instead using the project to do something else, to create a new part of the city, a public platform. That's the real success of the Tate Modern."  Herzog describes this process as "urban acupuncture", and as their busy studio attests, cities across the world are queuing up for a session. Their Serpentine pavilion is more of a head massage than a full treatment. It has been generated from traces of the previous 11 pavilions by the likes of Zaha Hadid, Frank Gehry and Rem Koolhaas, which the two architects "excavated" by superimposing drawings of their foundations. The result is a sculptural sunken seating area, like a freeform Roman amphitheatre, entirely clad in cork. Above it is a simple circular roof, which will fill with rainwater to form a shallow pool. "So we have architecture, we have form, without inventing it ourselves, which is typical of what we do," explains Herzog (De Meuron having rushed off to Hamburg).  The architects and Ai met more than 10 years ago. "We travelled together in China and saw things. Artist and architect collaborations have become kind of trendy, but they only work if they are natural and relaxed." Since Ai's arrest and detention by the Chinese authorities earlier this year, their relationship has been harder to maintain. Ai is not presently allowed to leave the country. Design discussions for the pavilion had to be conducted via Skype, says Herzog. "He is superfast at understanding things, though, so even with minimal gestures, he can make an important contribution."  One wonders how long Herzog and De Meuron can keep it up. Is it possible to stay "experimental" with so many big projects on the go? Can their urban therapy heal the world, one cultural institution at a time? As the firm has expanded, motifs have started to recur. They're fond of creating slopes that lead visitors into their buildings from underneath. They enjoy stacking up units haphazardly, like pick-up sticks. Their concrete spiral staircases have become a trademark, as has the archetypal "house" shape (a square with a pitched roof). Put these elements together and you might get a space-age science facility (like their Actelion Business Centre in Basel) or a playful furniture showroom (like their VitraHaus, nearby and very similar). Are they repeating themselves?  "There are projects similar to previous ones," Herzog acknowledges, "but they are still experimentally interesting because they reveal other sides of morphological elements. So yes, there are stacks, high rises, the eternal image of the house. But in every case, they have a different role."  Nevertheless, the 62-year-old has concerns for the future: "We are working in an interesting phase. We are at the end of modernity and at the beginning of something new. I think we can make interesting contributions." They are also thinking about what might happen as they get older: how to continue with younger partners, or if one of them dies. "What would he or I do alone? One would have to discover one's own range. We love to work together and involve ourselves in every design. How do you deal with change? We try to actively shape it and understand it, without meaning that we can always control everything." He laughs. "Even if, being from Switzerland, we are seen as people who control."  Herzog and De Meuron have been described as artists, scientists and even urban acupuncturists. Which is it? Herzog thinks it's simple: "Architects are just architects."  • The Serpentine Pavilion, in London's Hyde Park, opens 1 June. Steve Rose travelled to Basel courtesy of Swiss Air
Their wild, experimental buildings have made them in demand the world over. Herzog and De Meuron talk to Steve Rose about their latest work for Britain: a collaboration with Ai Weiwei