You rarely see animals in circuses these days.

No lions being tamed, no ponies being ridden bare-back by ladies in a scattering of sequins. Hold on a mo - is that a very large bear I see, scaling the Chinese pole with acrobatic flair? And are those bunny girls - but with actual big bunny heads? Are the animals back in the ring? Or could it be a trick of the light? A smoke-and-mirrors illusion? In fact, it's something altogether more brilliantly untoward and breathtakingly special: you're watching Circa going Beyond.

Last year, this Australian company of circus performers took the Fringe by storm with Wunderkammer, an hour sparked by high-flying, throwing-and-catching acrobatic technique wrapped up in sly humour, unexpected poetics and some very scanty costumes - altogether wonderful enough to bring Circa one of our Herald Angel awards for its chutzpah and brilliance.

This year, they're back with Beyond, a show that inhabits a territory somewhere between Alice in Wonderland and Darwin. And yet again Circa fields a group of artists whose bodies are as bendy, supple and risk-taking as director Yaron Lifschitz's conceptual imaginings.

It's a prospect that invites the sound of Grace Slick's voice to take over your thoughts, the lyrics of Jefferson Airplane's White Rabbit insidiously crystallising Lewis Carroll's story into a hallucinogenic trip.

It's not a song that features in Lifschitz's soundscore, however - nor is Beyond any kind of narrative re-telling of Alice's adventures. Rather it's an exploration of the "inner animalness" that we harbour under own skin.

This is when the references to Darwin start to rub shoulders with Carroll. And when Lifschitz describes himself as "interested in the idea of the creature and what our relationship is to the animal inside us and how that affects our lives", he's also saying that even when the performers are wearing bunny heads, or animal costumes, they are not pretending to be animals. The aim is to "create this flavour, this odd beautiful world where the lines between human and animal, day and night, all get a little bit blurred".

This aura of fuzziness does not apply to the Circa skills-base which remains firmly rooted in the paradox of human bodies being toned and trained to levels of uncanny expertise - and yet still intrinsically vulnerable and not immune to damage. Lifschitz wouldn't have it any other way. In all of the Circa shows he's developed since he took over the artistic direction of the original company in 1999, one thing has been missing: the kind of spectacular stage machinery that can almost supercede the performers' ability in grabbing audience attention.

In Beyond, you can't help but be aware of the people. You can see them sweat with the effort of physical and mental concentration - it's not just about flesh-and-blood strength, it's about focus, and maybe even a kind of animal instinct … that inexplicable accurate knowing, in the moment, where the other being is, or when to jump or catch. And when you're on a trapeze, or those slippery silks or a Chinese pole, you tune out of that zone at your own risk.

That kind of humanity on the brink of danger is a hallmark of what Circa brings to the stage. And sometimes, in past shows, there has been a whiff of the brutal and the extreme in the actions that take them - and us - to the edge. According to Lifschitz, Beyond is still intense, but in a different way. Words like "warm", "tender", and "generous" come into play and he describes it as having a "quite beautiful" emotional palette

"It's melancholy. It's very rich and very warm and the audience have a direct experience with that because there are people that perform with great honesty and great vulnerability - and taking risks and doing amazing things."

They do this to a musical collage that, typical Lifschitz and typical Circa, runs a gamut of genres from a crooning Sinatra to a brooding Nick Cave with - like the acts themselves - a few surprises thrown in.

And though Grace Slick's White Rabbit doesn't enter the arena, her words ring true for anyone watching the mosaic of images, themes and Darwin-esque questions that are the springboard for Beyond - Remember what the dormouse said: "Feed your head, feed your head"

Elsewhere, the Fringe programme mirrors the growing appeal of circus shows that bring new formats to traditional skills. Pants Down Circus: Rock does exactly what it says in the name.

The Australian show was inspired by Aerosmith, AC/DC, Joan Jett, Queen, Metallica and Bon Jovi, but this collaboration with fellow Aussie Scott Maidment - who directed Limbo, a sensational part of Edinburgh's Christmas 2013 programme - ensures the face-melting guitar solos are met with hard-core acrobatics, and some humour.

And if you feel like getting your skates on, then Wolfgang Hoffmann - the driving force behind Aurora Nova - has just the opportunity for you: This is Contemporary Ice Skating.

He explains that there are enthusiastically competitive ice-skaters showing off the art of gliding but says: "What's best is that you can get on the ice to play and dance.

"In my case it was in a joyful but not very elegant slip-and-stumble kind of way! It offers audiences a more visceral experience, and I find that important, as it has been my interest over the years to inspire people to move themselves and to understand and enjoy art not just intellectually but with their whole being."

Feed your head, or find your feet on ice - there are all kinds of circuses in town for the Fringe.

Circa is at Underbelly Bristo Square (July 30 - Aug 25); Pants Down Circus: Rock is in Assembly George Square Gardens (July 31 - Aug 25); This Is Contemporary Ice Skating is at Murray Field Ice Rink (Aug 3 - 23: dates and times vary).