When Lady Gaga embarked on the early stages of her Monster Ball tour in 2009, it marked the provocative pop princess's crossover into the major league, with a spectacular show described by some as the first ever pop electro opera.

In its look, however, Monster Ball also unwittingly formed a bridge between a pub theatre in Shepherd's Bush, art-punk band Wire, the Royal Opera House, lingerie label Agent Provocateur and the closing ceremony of the 2012 Olympic Games. All of these, including Monster Ball, featured the work of theatre designer Es Devlin.

Fans can get a taste of her work for Monster Ball in Transformation and Revelation: Gormley to Gaga – Designing For Performance, an exhibition of 33 British designers which opened at Summerhall in Edinburgh this weekend.

"It was a very interesting point in her trajectory," says Devlin. "For Monster Ball we were given an initial budget, then almost every day it went higher. It was designed for a specific size of stage, but as Gaga's popularity grew, she started being able to sell out arenas. The first night was in an arena in Montreal, and I don't think it would be as thrilling to get involved in a moment like that now. There's nothing quite like being there at that first moment of a new energy in art."

As well as Devlin's work, the exhibition features designs for dance by sculptor Antony Gormley and Rae Smith's design work for the original National Theatre production of War Horse. The mix of models and drawings contained in a series of purpose-built vitrines spread out across Summerhall was originally seen by almost 150,000 people during its run at the V&A museum in London earlier this year.

Organised every four years by the Society of British Designers as a showcase for the best of British design, this year's exhibition was initially shown in Cardiff, with 206 designers contributing.

Thirteen of these were selected to represent the UK at the Prague quadrennial before being expanded to its current scale.

"Theatre design is a backstage profession that never really gets exposed," says curator Peter Farley, "and one of my bugbears is that all too often the director gets the credit. Stage design isn't just about decoration. It's about adding another visual narrative to everything else that's happening on stage. What I'm pleased about is putting theatre designers and artists into a fine art context, but we have work by architects, sculptors, painters and designers, so the edges are blurred."

Devlin is a perfect example of this. Having studied music from a young age, she first gained a degree in English literature before embarking on a fine art foundation course at Central St Martins College in London, where she moved onto the stage design course. It was while at St Martins in 1992 that Devlin assisted Damien Hirst on Agongo, an installation presented at the Richard Demarco Gallery.

Devlin won the Linbury Prize for Stage Design, embarking on her first professional job in 1995 directing a production of Edward II set in a swimming pool for the Bolton Octagon Theatre. This led to work at London pub theatre, The Bush, then being run by Mike Bradwell, who hired Devlin to design Mark O'Rowe's breakthrough play, Howie The Rookie, which transferred to the Traverse Theatre for an Edinburgh Festival Fringe run in 1999.

Devlin worked with Max Stafford-Clark's Out of Joint company, designing a revival of Andrea Dunbar's play, Rita, Sue And Bob Too, as well as a remarkable African-set take on Macbeth. Both of these visited the Traverse, with Macbeth occupying the claustrophobic Underbelly space.

Rae Smith also has Scottish connections, and, long before War Horse, designed shows for TAG, 7:84 Scotland and The Tron. Smith has chartered a similar trajectory to Devlin, who has moved from the National Theatre, the RSC and English National Opera to Pet Shop Boys musical, Closer To Heaven, David McVicar's production of Salome for the Royal Opera House, and a series of steamy ads directed by Mike Figgis for high-class lingerie brand, Agent Provocateur.

Devlin's move into music came after Edinburgh-born director of the South Bank, Alex Poots – currently in charge of Manchester International Festival and the biannual Armory Show exhibition in New York – approached her to provide a set for art-punk band, Wire, in parallel with Jake and Dinos Chapman.

"It was pretty much impossible for them to perform in," Devlin says. "They couldn't see each other, they couldn't hear each other and they couldn't get out, but it looked good."

It looked good to Kanye West, who was impressed enough by Devlin's contribution to the Wire show to hire her to design his 2005 Touch The Sky tour. "Again," says Devlin, "it was a very interesting time to be working with Kanye, and the nice thing about that is a working relationship has developed, and we're going to be doing something next year. Kanye's got a mind that moves at the speed of light, and he gets impatient with people who can't keep up, so it's good to have a shorthand with him."

Devlin has gone on to work with Muse, Mika, Goldfrapp, Nitin Sawhney, Take That, Lenny Kravitz and Rihanna. As with West, Devlin has continued her working relationship with David McVicar, and in 2014 will be transferring his production of Les Troyens to La Scala in Milan. In the meantime, Devlin may skirt around her involvement with epic flop Batman Live, but her contribution to the Olympic closing ceremony is clearly something of a pinnacle. "Everything seems very easy now compared to the London Olympics ceremony," she says. "I was delighted I was involved in that moment of history. But it brought with it enormous pressure, because we were constantly having to rework things as we went along.

"It would have been wonderful if necessary if we could've had control of things from the beginning, but the music industry hierarchies don't work like that, and sometimes the result of that was disappointing. Let's just say that some of the artists really got into the spirit of the event, while others just wanted to play their song. You wanted to say to them, can't you put your own sense of self-importance aside for one minute and play that song from 1986 that says something about British culture."

Devlin may or may not be talking about George Michael, who premiered a new song at the event. Even with such dealings with pop divas, any further collaborations with Lady Gaga sound unlikely.

"I think she's kind of munched me up and moved on," Devlin says. "I think she's probably munched a lot of people up. Maybe she'll run out and have to start again."

Transformation and Revelation: Gormley to Gaga – Designing For Performance, Summerhall, Edinburgh, until February 22. Visit www.summerhall.co.uk.