Behind the scenes at Cirque du Soleil

You have to adjust your sense of scale to appreciate fully the phenomenon of Cirque du Soleil. Its founder, the bald, puckish (and very rich) Guy Laliberté describes it as "the No 1 entertainment company in the world" – a grandiose statement sure to raise the hackles of any Cirque cynic. But then you look at the evidence. Since its humble beginnings as a rag-tag gang of stilt-walkers and clowns on the streets of Quebec in 1984, Cirque du Soleil has played to nearly 80 million spectators in 200 cities across the globe. Its 4,000 employees come from more than 40 countries and shows cost millions to produce. The most expensive, KÀ, cost $200m (£138m) in 2005 – more than most Hollywood blockbusters. The Cirque experience is as much about the eye-boggling statistics (number of wigs used, height of the stage rigging, size of the sound system) as it is about spectacle. The only number that is not readily to hand is the privately held company's worth but estimates put it at more than $1bn. This is theatre, supersized.

Tonight, Quidam arrives at London's Royal Albert Hall for its UK premiere ahead of a four-month tour. The story of the piece, according to its website, is as follows: "A young girl fumes; she has already seen everything there is to see, and her world has lost all meaning. Her anger shatters her little world, and she finds herself in the universe of Quidam." As plots go, it's off-puttingly abstract but then Cirque's unique fusion of theatre and circus doesn't really work on paper. It's best to ignore the "plots", the statistics and the mission statements and concentrate instead on the wonderfully outlandish costumes, slick stagecraft and, most of all, the jaw-slackening feats of physical prowess on stage. In the case of Quidam these include women entwining themselves high in the air in crimson silk drapes, men swinging from hoops with vertigo-defying ease, improbably high human pyramids – and, of course, clowns. While it's easy to be cynical about this global superbrand, dismissing it as McTheatre, its absurdly high production values and awe-inspiring performances turn out to be irresistible in the flesh.

There are currently 18 original Cirque shows running around the world. Of these, seven are touring shows, including Quidam, and 11 are resident shows – in Las Vegas, Orlando, Macau and Tokyo. The latter are created specifically for their environments and will only ever be seen there. For the true fan, then, a trip to Las Vegas is mandatory. The city of sin has become the spiritual home of Cirque, hosting six shows at various hotels on the Strip. Their first was Mystère, a fairly traditional circus set-up which is still going strong after 15 years. It was followed by O, a fabulous water-themed production that pushed Cirque far beyond the boundaries of any ordinary circus. Opening in conjunction with the Bellagio in 1998, the show was built into the hotel (at a cost of £100m) to reflect its aquatic theme. Featuring a 1.5 million-gallon tank that can change from pool to stage at the flip of a switch so that the performers frequently appear to be walking on water, O has synchronised swimming, high dives (from the 60ft rig), contortionists and trapeze artists swinging by one foot, 20ft above the stage. It is quite breathtaking and impossibly beautiful.

Since then Cirque has opened Zumanity – a sensual revue attempting to bridge the gap between theatrical entertainment and Vegas's more traditional night-time pursuits – and KÀ, the Robert LePage-directed epic at MGM Grand. In 2006, it premiered Love, a Beatles-themed show, which marked the first time Apple had licensed the music to be used in a theatrical partnership. The result is as moving as it is eye-widening. In a 360 degree spectacular, parkour artists scamper to "I Wanna Hold Your Hand", rollerbladers speed up and down ramps for "Help!", and "Lucy in the Sky with Diamonds" is given a gorgeously trippy aerial ballet. The Fab Four, remixed by George and Giles Martin and thumping through 6,509 speakers, have rarely sounded better.

That Cirque du Soleil has grown from Laliberté's lowly beginnings as a fire-breather, working the pavements of a small town, Baie-Saint-Paul, outside Quebec City, to having the monopoly on non-gambling or adult entertainment in the most overblown city on earth is the key to this weirdly schizophrenic company. It's also the secret of its success: for all the billions poured into it, Cirque remains at heart an old-fashioned circus, with performers dedicated to honing their eccentric acts and a Heath Robinson-esque approach to creating the stunning visuals. When I ask O's company manager, Tony Ricotta, about a climactic coup de théâtre in which the curtain becomes a hot air balloon, he confides that "it was designed on a napkin in a diner". Backstage at O, I am shown intricate hydraulic machinery, underwater speakers and the hi-tech, charmingly named aqua coulisses (underwater wings) where performers take gulps from oxygen tanks before they appear from the depths. But there are also the practicalities – hot showers in the wings, towering piles of wet towels, a gym with weights where the performers limber up and, in the costume department, a battalion of women ironing and stitching the Lilliputian net and lycra costumes and fluffing up the multicoloured, dreadlocked wigs.

The performers are at the top of their field – a Cirque cast will typically include Olympic athletes, swimmers or gymnasts who have turned professional, traditional circus folk and stunt-people. Having been scouted out at festivals or had their video auditions accepted, fledgling Cirque stars are then shipped off to the Montreal HQ where they are given a three-month "general formation", learning jeu (clowning) techniques, dance and improv skills. "We take athletes and make them artists," says Krista Monson, head of casting, who oversees Cirque's database of more than 38,000 artists, which includes street dancers, ballerinas, acrobats, divers, parkour champions, contortionists and Russian Swing experts. She receives more than 1,000 audition tapes a month. "We're looking for people who are comfortable doing what they do but who are also open to being a fool."

This is central to the Cirque ethos, which remains a strong creative driving force. Laliberté, though increasingly "hands off" creatively, still has the final sign-off on all shows, demanding complete artistic and financial control. The company received no private or public funding from its early days in 1992 until it sold a 20 per cent stake to two Dubai-based investors, Istithmar World and real estate developer Nakheel, for an undisclosed sum last summer. Laliberté announced firmly at the time that he was still very much "the captain of the ship".

Cirque's latest venture is Criss Angel, Believe, at the Luxor in Las Vegas, the first time it has incorporated magic (another Vegas staple). The $96m show is essentially a vehicle for the popular television magician Criss Angel, a kind of emo David Blaine with long black hair held back by a bandana and kohl-rimmed eyes, whose Mindfreak show sees him performing illusions – juggling chainsaws, being steamrollered on a bed of broken glass or levitating in the beam of light which shines out from the top of the Luxor's pyramid – to a heavy metal soundtrack.

The show itself is an enchanted love story with whimsical Alice's Adventures in Wonderland and Wizard of Oz motifs and some very cool street dancing rabbits, courtesy of Britney Spears's choreographer Wade Robson. "It's magic with emotion," says its director, Serge Denoncourt. "Not so much tah-dah and girls in short skirts." The traditional magic tricks – cutting Angel in half with a chainsaw, the release of hundreds of doves into the air – are performed with expensive panache but there's little for the Cirque troupe to add to the mix and the show never really takes off. "Cirque doesn't work with stars," said Laliberté after the premiere. "It's not an easy thing to do. We are a collective." Therein lies the problem. In trying to push the envelope by relying on illusion and fakery, Cirque has betrayed its fundamental selling point – performing the nearest thing there is to real magic with real human bodies.

Still, it's a rare false step. Next up is an Elvis-themed extravaganza in – where else? – the heart of Vegas. Cirque bought the rights to the King's back catalogue from CKX, Inc two years ago and the show is slated to open at the new MGM CityCentre hotel in December. Negotiations to bring Cirque to the UK – both Battersea Power Station and the O2 have been mooted as bases – are still ongoing. After that LePage is returning to create another new show, a movie-themed show that will open in LA, and, in 2011, Cirque will put down roots in another desert, at Dubai's Palm resort. In other words, nothing less than total world domination awaits Laliberté and his motley troupe. Not bad for a bald firebreather from Quebec.

'Cirque du Soleil: Quidam' appears at the Royal Albert Hall, London SW7 (020-7589 8212) until 8 February; then touring to 19 April (www.cirquedusoleil.com )