These are strange days for purists. In almost every area of the arts, genres are spilling into each other, cross-pollinating, refusing to remain in neat boxes. You go to the theatre expecting actors under a proscenium arch, and you get videos, animation, and intricate dance routines. Go to the opera expecting corsets and coloratura, and you get electric guitars and costumes designed by Viktor & Rolf.

Rock musicians are penning operas (Damon Albarn, Rufus Wainwright), performing with orchestras (Metallica, Elbow) and learning the lute (Sting). Theatre companies such as Punchdrunk are staging strange shows that feel more like exhibitions, or dismembered film sets, than plays. Film actors are learning to dance (Juliette Binoche); choreographers are acting (Akram Khan). In between judging TV talent shows, pop impresario Simon Cowell is hothousing classical acts (the Armani-clad quartet Il Divo and their pre-teen equivalents, Angelis). In fact, "classical crossover" is now so big, the US magazine Billboard has given the category its own chart.

Of course, the arts have a distinguished history when it comes to collaborations: Diaghilev's ground-breaking Ballets Russes worked with artists and composers such as Picasso, Joan Miró and Stravinsky, while the 1970s saw rock acts like Deep Purple and Rick Wakeman experimenting with classical.

But the distinctions between genres have never felt quite so blurred as they do now. In theatre director Katie Mitchell's words, the world is no longer "neat and organised and tidy"; it is fractured, multicultural, multimedia - and artists want to capture this. They know their audiences move easily between "high" and "low" culture, and that their attention shifts with the click of a mouse.

Call it crossover, call it fusion - the fact remains that it can be challenging, these days, to leave the theatre, concert hall, or art gallery with any idea as to how you might categorise what you saw. And for many of us, this is exactly what makes the contemporary arts scene so exciting. But what is it like for the artists who set out on these genre-bending projects? Is the process a happy, collaborative one - or a frustrating battle of egos and visions? We talked to four partnerships to find out.

'He's used to knocking out a show. My last one took a year and a half'

Daniel Kramer, director, and Frauke Requardt, choreographer

Pictures from an Exhibition, this pair's first collaboration, is inspired by Mussorgsky's piano suite. Fusing music, dance and drama, it premiered at London's Young Vic last month, and will be at Sadler's Wells next year.

Daniel on Frauke: Leaving the ego outside the room is a huge challenge. At the beginning, you're like: "This has to be about me. This is my show." But once you realise the other person isn't there with a knife to cut your ideas down - that they want to question them to make the show stronger - then you think: "Thank God there are two of us."

We did a week's exploratory work with 12 dancers before starting our show. There were definite question marks about whether it was going to work. Directors and choreographers both edit what performers create; we're used to leading a room. So every time I started to lead, Frauke would feel redundant. But by the end of the week, we'd found a way to tag team together.

We like work that's quirky, visceral, guttural, that asks emotional questions and isn't intended to run on Broadway for five years. The way I direct is very physical, so it wasn't a huge departure to direct dancers. I grew up on an Ohio sheep farm, studied dance and learned how to throw myself around like an animal. I direct an actor so that you can see every impulse in their spine. I'm obsessed with the poetry of the body. Dancers' bodies can create magic.

I'd describe our work as shape-shifting, metamorphosis, or transmutation. I'm from the MTV generation: we're used to being accosted by changing images, pop music, blockbuster art. But with a collaboration like this, you have to ensure the vision of the piece doesn't get diluted. Somebody has to be driving the car. Officially, I have the keys. But we're on a long trip, so we have rest stops. Sometimes Frauke drives.

Frauke on Daniel: The first week of working together was traumatic. I'd invited the dancers, most of whom I've worked with for a long time, so I was asking for their trust with this new direction. Daniel wanted to show that he could run a room of dancers. Somehow we muddled through and, at the end of the week, looked at the scenes we'd created, and saw there was something there. It was going be all right. I think we fell in love with each other a little.

There's a desire for the extreme, for ugliness, in Daniel that I don't fully share. Otherwise, our aesthetics are similar; we managed to tie them together. We work in opposite ways. Daniel's from a much more commercial world: he's used to knocking a show out in five weeks. He's a machine. My last show needed 15 weeks of rehearsals, spread out over a year and a half. He likes to work within a defined structure, and he's always over-prepared.

I understand why people need to label art, otherwise they don't know how to read it. But I don't want to make something that's just called a dance piece. It should just be a piece of art.

'There are 2,000 muscles in the face. Leo's camera can show this'

Katie Mitchell, director, and Leo Warner, video designer and cinematographer

In Mitchell's fast-moving shows, filmed sequences are recreated live on stage. She's worked with Warner on six pieces, from 2006's Waves, based on Virginia Woolf's novel, to this year's After Dido, based on Purcell's opera Dido and Aeneas. Their next show is a version of Nono's opera Al Gran Sole Carico d'Amore, to be performed with the Vienna Philharmonic at the Salzburg festival in August.

Katie on Leo: It's very clear that I'm the boss. We never clash. I first met Leo when I needed a video designer for Waves. He'd just worked on Black Watch, a big hit, and someone at the National suggested him. The deadline was tight: we were two weeks into rehearsals. There was no time for talking. We had to start working with the actors right away.

Leo doesn't just do video design; he's also a brilliant director of photography. In a video designer, that's unique. He has also tailor-made the technology we use. It's all enormously complicated, and I'm hopeless technically. Film can tell a story more deftly than theatre: it moves across time and space, bringing the audience much closer to the acting. There are 2,000 muscles in the face alone. In most theatres, you're too far away to see this level of detail, but the camera can show it.

Some people have problems with our work. They describe it as "multimedia", which is very vague. Or they say it's about "sensory overload". But I've lost faith with traditional theatre, linear narrative and the well-made play. I use sound, music and video to more accurately reflect our perception of the world - it's not neat and organised and tidy. For me, looking at live performance is like looking at a canvas. And I want every bit of that canvas to be alive.

A collaboration like this raises everyone's game. It takes an artist out of their comfort zone, makes them create differently. Thanks to Leo, I am now talking to a different audience. Much younger. And that's a beautiful thing.

Leo on Katie: I do my best work with Katie. There's such attention to detail - we might spend a day working on one shot. She sees things in terms of character which I am prone to overlook. Conversely, what she gets out of me is an ability to get closer, to focus in.

Katie had been experimenting with film in a primitive way. I was encouraged to think like a film-maker, free from the constraints that people in theatre have. Our work has got more complicated. We've pushed our mediums to the limit - especially with After Dido, which contained sequences I wasn't 100% thrilled with. There were continuity errors, but most of the film is of cinematic quality.

I talk of our work as a hybrid between film and theatre. The people who hate it - and there are quite a few - tend to either watch the screen or the stage, yet neither is designed to stand alone. We don't set out to confuse people. People talk about killing off traditional theatre, but I have no idea what that is. After six shows, I've decided to stop worrying about it. Some people simply don't engage with our work. That's fine.

'Deep down, I think David would love to smash guitars up on stage'

Ray Davies, musician, and David Temple, director of the Crouch End Festival Chorus

Davies and Temple met in 1998, when Temple organised the choir that performed Davies's first choral composition, Flatlands. They've since worked together on choral arrangements for the 2007 BBC Electric Proms, and on the Kinks Choral Collection, an album of choral versions of Kinks songs released on Decca next week.

David on Ray: I first heard You Really Got Me on Top of the Pops when I was 10. Ever since, Ray's been a legend for me. So when the phone rang in 1998 and this voice said, "This is Ray Davies, have you heard of me?", I was shaking. The first time I met him was the most exciting day of my life.

Choirs shouldn't sing pop music. It just doesn't suit them. That's why we went for this wall-of-sound, backing-vocal style. My choir has a very clean sound; it's not a heavy, operatic warble. I think most people like it, even if they don't particularly like classical music.

As the composer, Ray had to be the final arbiter on the arrangements of the songs on the album. But he was very respectful of what I do. During the final recording sessions, he came out of the control room, and the choir erupted - but Ray tried to deflect all the credit back to me. I was really touched.

Teaching a choir a new piece is very different to a band learning a song. With a choir you have to be more organised. And the classical and pop worlds use different terminology. It took me a while to understand what Ray was talking about when he said something was "a bit pitchy". I think he meant out of tune.

I can't bear crossover projects when they're done to make money or make people famous. They have to have the art itself at the core.

Ray on David: I sang in the choir at school, and did a course in orchestration when I was with the Kinks. But it was only when I wrote Flatlands that I realised how interesting choirs can sound. The choral versions of Kinks songs we did at the Electric Proms were a big success. David rang me up and said: "You should do this as a record." I had to think about it. I knew I didn't want to get into doing Kinks numbers in a sing-along, Black-and-White Minstrel style. I wanted to do justice to the choir - stretch them, use their colouring.

I didn't want the record to be pretend classical music, but something that's worthy of a second listen. We started with Shangri-La. It was all oohs and aahs so I said: "Let these people sing!" With rock music, you just pound away, putting compressors on the sound. But that would have killed the choir's ethereal quality. So we went for that wall-of-sound style, with no double tracking. Some bits might have taken Phil Spector seven tape recorders - and 15 gunshots.

David's a great teacher. He brings people together with a lot less bloodshed than we used to have in the Kinks, though deep down, I think he would love to smash a few guitars on stage. Some of my songs have really grown on me in the new versions. The ones from the Village Green Preservation Society have great choral moments, while You Really Got Me has retained its anarchic edge, but through subtle harmonies. Is it crossover? I'm not sure. It is what it is.

'I like the word crossover. We really did step into each other's worlds'

Idris Khan, artist, and Sarah Warsop, dancer and choreographer

Khan and Warsop were introduced by choreographer Siobhan Davies and gallerist Victoria Miro in order to create a new piece for The Collection, a series of collaborations between visual artists and dance-makers. Their resulting video installation, Lying in Wait, is at the Ikon Eastside Gallery, Birmingham, from 24 September to 4 October (0121-248 0708).

Idris on Sarah: I don't know much about dance. In fact, I don't know anything about dance. But I'm far more interested in it now, having worked with Sarah.

There was a language barrier at the start. At every meeting, there came a point where I was a little confused. You can enjoy contemporary dance for what it is, as an innocent bystander, but when you know what it takes to understand the body in that way, it's phenomenal. Sarah can work on one subtle move for an hour. Filming her was the easy bit.

We work along similar lines. Sarah structures codes and sentences in her head as she creates a dance. I'm interested in that kind of repetition myself. I don't influence Sarah's choreography. I was there to make the film. At one point, she wanted to get involved in editing, and I had to say: "Look, I've got to do this on my own." She was fine about that. You've got to have trust.

I don't think we made a dance, a film, or a dance film. It's a performance. Or an installation film. I don't know. I still confuse myself. But I do think the viewer gets something out of this that they wouldn't from just watching Sarah on stage. Some movements are slowed down, others accelerated, which gives them new emotion and narrative. You can appreciate the dance more as it's happening. Once it's gone, it's gone.

Sarah on Idris: Idris layers up imagery, with meticulous repetition. I had this instinctive sense that I would like to meet this person. When I did, we were checking each other out, thinking: "Is this going to work?" I don't know why, but I was confident that it would.

You have to be quite humble - to step back and let someone inform you, always ready to say: "Could you explain that again?" Otherwise it becomes a battle. Idris respected my knowledge of dance, and I respected the fact that, in the editing suite, he sees things I don't. We informed each other - and, I hope, took our art forms to another level.

I like the word "crossover". We really did step into each other's worlds. The longer you perform in one area, the more you want your work to be seen by people beyond it. And it was interesting to see reactions to our film. People are often a bit scared of dance - there's a feeling that you don't understand, that you're getting it wrong. But people were taking their time, wandering through the gallery, taking a really close look at the film. Some said they found it quite full on, being faced with a full-sized image of a human body. But that's what the work's about: the fact that, ultimately, we all have this amazing body, yet we take it so much for granted.

Fantasy pairings

Our critics pick their dream collaborations

Zaha Hadid and Oasis

I'd like to see Oasis write a song inspired by one of Hadid's buildings. Forced out of their thuddingly conventional comfort zone, Oasis might come up with something amazing.
Caroline Sullivan, pop critic

Javier de Frutos and Prada

I'd have them reinvent Le Train Bleu, Diaghilev's portrait of Cote d'Azur's bright young things. De Frutos could do a flamboyant take on body culture as Prada unveils beachwear.
Judith Mackrell, dance critic

Erich von Stroheim and Richard Strauss

Strauss's scores are the musical equivalent of Stroheim's ornate movies. The idea of Stroheim filming Salome or Elektra is the stuff of my dreams.
Tim Ashley, classical critic

JS Bach and Francesco Borromini

When I listen to Bach's Goldberg Variations, I picture Borromini's spiralling staircase in the Barberini palace in Rome. Bach's music is architectural, while Borromini's work is musical.
Jonathan Jones, art critic

Sylvia Plath and New Order

Had Joy Division replaced Ian Curtis with Plath, her similarly bleak world view would have allowed them to build on the compulsive themes of second album, Closer (though not the disco hits).
Dave Simpson, pop critic

Steven Spielberg and Richard Wagner

I'd challenge them to come up with the ultimate multimedia experience, a fusion of all the arts that would dwarf even the Ring cycle in its wizardry. Tom Service, classical critic

Pina Bausch and Bruce Nauman

Their differences as well as what they share - humour, threat, tenderness, wonderful use of space, movement, sound and an uncompromising individuality - would make the sparks fly.
Adrian Searle, art critic