Ai Weiwei, probably contemporary China’s best-known artist, and Steven Spielberg, probably America’s best- known filmmaker, have both resigned as artistic consultants to this year’s Beijing Olympics. The former cited the Chinese authorities’ inclination to make the games into a “propaganda show” (raising the question of what exactly he had expected). Spielberg took a stand against China’s support of the Sudanese regime, arms for oil, and the ongoing horror show of Darfur. But, so far, the Olympics still has Cai Guo-Qiang. The most visceral, the most challenging and the most fascinating of China’s first wave of internationally recognised and now hugely successful artists, Cai promises to make the opening of the Beijing games a real blast.

Cai Guo-Qiang (it’s pronounced “psycho chang”) made his reputation with a medium all his own, his “Gunpowder Drawings”. Stunning works formed by the physical impact of explosions, these blackened surfaces are the haunting shadows created by the ignition of a fuse and the consequent explosion of a gunpowder charge. They are works that capture the brief but palpable moment of time between ignition and blast, the negative recording of the intense flash of light, the black yin to the white yang of the event itself. The “drawings” – which reflect on the Chinese invention of gunpowder, its traditions of pyrotechnics, of the contrast between dark and light and of the fleeting essence of a moment in time – have become one of Chinese art’s most powerful and recognisable manifestations yet they represent only a fragment of the work of one of the most profound and interesting artists on the contemporary scene. A quick spin up the spiral ramp of New York’s Guggenheim Museum reveals how deep and reflective that work can be, encompassing themes of history, ideology, politics, mythology, religion, technology and beyond.

Born in Guangzhou in 1957, Cai Guo-Qiang has lived in New York since 1995 so it is appropriate that this, his first major retrospective show in the west, is in his adopted city. But, given the fabled restrictions of Frank Lloyd Wright’s magnificently inflexible space and the constantly changing formats, media and scale of Cai’s work, the Guggenheim might seem an odd choice of venue. From the first glimpse of his extraordinary installation, “Inopportune: Stage One”, any fears are allayed. The work is a collapsing tower of cars, a series of nine real automobiles tumbling through the atrium, ornamented, if that is the right word, with twinkling light tubes translating the visual language and chaos of an explosion, of a car bomb, into the banal domestic language of Christmas decorations or commercial illumination. The original work inhabits the lobby of the new Seattle Art Museum (which opened last year). While it looks fine there in a big, neutral, modernist space, somehow in the controlled cylinder of the Guggenheim it produces a more violent image. We are always reading about the “spiral” of violence in Iraq: there is something tragic about a downward spiral, and here it is.

The absurdly gently twinkling lights of the explosion give way to another installation that uses the architectural space to great effect, “Inopportune: Stage Two”. Here, cars give way to tigers. While the cars are exploding as they fall through the air, the tigers are pierced with arrows, Saint Sebastian-style. They evoke the dream tigers pouncing from Dalí’s canvases and apparently refer to a Chinese legend of a bandit who saved a village from a man-eating tiger and became an unlikely hero. The installation is lent a real poignancy through its juxtaposition with a delicate, traditional Chinese painting by the artist’s father, Cai Ruiqin, depicting 100 tigers. The artist’s father is a dedicated communist, working in a state-owned bookstore; these generational contrasts and thoughtful little rebellions are found scattered through the show.

Behind the tigers, “Borrowing Your Enemy’s Arrows”, a suspended raft spiked in similar porcupine style, similarly refers to the legend of a general who had run out of arrows and sent out a boatful of straw dummies in order to attract a barrage of archers’ fire, replenishing his army’s arsenal. A single red Chinese flag flutters at the rear of the craft in the breeze created by a whirring electric fan. This, we are told, refers to the Chinese proclivity to steal and adapt western technology and appropriate it. The same backstory applies to “Cry Dragon/Cry Wolf: The Ark of Genghis Khan”, in which a raft of sacks is crafted into the form of a dragon, here augmented by three buzzing Toyota engine blocks.

But perhaps most striking of all the installations is “Head On”, 99 wolves winding their way around the ramp, each leaping higher into the air until suddenly they smash into a glass wall and collapse into a heap on the floor. Conceived for a show in Berlin, the dimensions of the original glass wall were based on those of the less transparent Berlin version. There is no need for explanation of the metaphor here, it hits you as hard as the wall hits the wolves. The work is part of a critique of man’s inclination to be seduced by mass ideology.

They also, in this American setting, can’t help but evoke the coyotes of Joseph Beuys. In his almost shamanistic 1972 action, “I Like America and America Likes Me”, Beuys spent three days in a room with a coyote in a search for the essence of the nation, communing with the spirit of an animal revered by the Native Americans. In this light, perhaps Cai’s installation means something more: is there a critique of consumerism and globalisation in there too?

The arresting installations slowly give way to the artist’s older works, the gunpowder paintings and paintings made using a fan to blow paint across the surface of a canvas. Each of these seems a kind of alchemical process, a method of capturing the essence of an ineffable element, fire or air. The results can seem capable of recalling a range of imagery, from the Turin shroud to abstract expressionism. The best of the works have an extraordinary power; others desperately need their explanations but once those associations are planted they seem to blossom into a thousand other avenues of meaning. It is the videos that work least well. The power of explosions has been so thoroughly hijacked by Hollywood (and by terrorists) that the real thing, made art, looks puny by comparison.

The power, scale and vision of Cai Guo-Qiang’s work seems unsuited to the Guggenheim. Yet something about that spiralling ascent, moving through the media from installation to drawing via film and explosion, suggests an almost Buddhist progression. While some works would undoubtedly benefit from more space, the quick-fire intensity of so many media and so many ideas on such a short, truncated journey intensifies the impact. It is easy to become cynical about the outrageous hype that surrounds Chinese art, as well as about artists who continue to criticise China from across the Pacific while accepting prestigious state commissions from their homeland. This major exhibition will help dispel at least some of those doubts. Cai Guo-Qiang is one of the most intriguing artists working today and, for the first time in my life, I can genuinely say I am looking forward to an Olympic opening ceremony.

Cai Guo-Qiang’s ‘I Want to Believe’ is at the Guggenheim Museum, New York, to May 28