Long before the end of Circa's Wunderkammer - which is part of this year's Underbelly Fringe programme - your heart is thumping like a wild, untutored drum solo.

And it's more than sheer (often nail-biting) amazement at what's unfolding before your eyes, as bodies flick through space and then click together like pieces of a jigsaw or else defy gravity to execute a piece of cunning whimsy. Striptease on a trapeze, any one?

Because layered into the adrenalin rush that makes you catch your breath is a longing that surely harks back to childhoodand the "running away to join the circus" pipe-dream that lifted your hopes beyond the grown-up future you sensed would be more work than play.

Your head, of course, has already informed your heart that this bright-eyed yen is a no-go. Yes, you have the strength to hold a mobile phone to your ear for hours on end - but could you be the base of a human tower with six other bodies on your shoulders? As for trusting other people to use you like a human ping-pong ball, throwing and catching and throwing you back and forth at speed? Or that thing - which I won't specify in detail - about balloons and …erm, noses?

Getting into harness with the Brisbane-based Circa is a dream that only becomes a reality for a very few. Add up the numbers currently performing all across the globe, and the full ensemble is a corps of 21 - although their versatility and expertise across the spectrum of traditional circus skills easily rivals (and probably outclasses) the acrobatic fire-power of much larger organisations. A troupe of seven will bring Wunderkammer to Edinburgh, the first time Circa has been back in the city since they wowed audiences in 2009. Lewis West was part of that first Fringe showcase. Simply entitled Circa, it was a kind of compilation-sampler that introduced audiences to the way these Aussies have of doing things. West, who will be one of the Wunderkammer seven, sums it up as "striving to bring out the humanity of it. We don't hide behind make-up, or flashy props, or incredibly fancy-spectacular set designs.

"It's all about real people doing amazing things - and making audiences feel something more, something different, from what they probably expected of a circus show."

This is not some idle boast from a loyal Circa trouper. Words like "moving", and "poetic" or "profound and philosophical" don't only creep into highly-starred reviews: they get scattered through audience feedback comments and blogs. Responses can, in fact, get quite emotional and slip into accolades of the "I was deeply moved" intensity you might associate more with theatre than with circus. There's an irony here that isn't lost on Circa's director, Yaron Lifschitz.

Ask him why he joined the circus and he'll reply: "Because I failed at making theatre. I was really, really bad. And when I realised that - and realised that what was happening on-stage was kind of false, and so for me rather boring - I had to find another path. Anyway, somehow I just lucked into the circus.

"I went for a job interview and they gave me the job even though I told them I didn't really like circus. Maybe what I meant was I didn't like show-offs: the featuring of genuinely difficult tricks, but just for the sake of showing off your ability to do tricks. That just feels empty to me. Or the kind of bells-and-whistles glitz that overrides everything else, including the people performing. And I do know that we're often described as "lo-tech", but one person's lo-tech is another person's carefully stripped back because nothing should be taking meaning away from a moment, or the audience's attention away from where it should be - on the performer."

In Wunderkammer, there's very little danger that your attention will drift away from the Circa performers.

For one thing, Libby McDonnell's sexy costume designs are definite eye-ticklers: little snippets of lace and satin in black, red and white that seem held together by will-power and fastenings that disengage with a nod and a wink. The strongest erotic charge, however, is in what those Circa bodies do fully-clothed or otherwise. You could say their finesse, the purity of body-lines that make airborne acrobatics look like calligraphy in space, and the unpretentious way they engage with obvious danger, deliver the juiciest kind of tease because it's underpinned by Lifschitz's emphasis on being honest and authentic. If you're at the top of your game - as these artists are - you don't need to show off, or be hyped up by introductory fanfares or a build up of drum rolls.

At one point, Lifschitz is talking about how a show like Wunderkammer takes shape. He's thrown all kinds of source material into the melting pot: fugues, both as in music and mental states; quantum mechanics and instability; burlesque and vaudeville - a mix of likes and dislikes that will act as provocations when he and the performers head into the studio to try out ideas. "That's when it gets a bit like physical jazz," he laughs. "You're looking for those moments, those interactions, that don't arise from following any kind of narrative - they're like happy surprises, and they work because they reach out and touch you. Maybe make you laugh, or - and this has to be a core part of what we do - just marvel at the beauty of it before it passes. The sheer wonder of what a human being can do with their body. And we came up with Wunderkammer."

Circa are performing Wunderkammer in the McEwan Hall, at Underbelly Bristo Square to August 26 (no performances on August 7, 13 and 20).