The choreographer Lin Hwai-min founded Cloud Gate Dance Theatre of Taiwan in 1973. His dancers are nothing if not dedicated to his ideals, with a training programme in t’ai chi, meditation, martial arts, Chinese opera movement, modern dance, ballet and calligraphy. Presumably, they manage to fit in a bit of sightseeing on their extensive tours. Last week’s visit to the Barbican — for Bite09 and the Dance Umbrella festival — with their 2006 production Wind Shadow, was Cloud Gate’s sixth London appearance in 10 years. Previous stagings have left vivid impressions of visual beauty, with devices such as a rain of golden rice, reflections on a flooded floor, bamboo, live inking scrolls, in all of which the dancers are elements in a theatrical, evolving art installation.

The concept and visual direction of Wind Shadow are by the artist Cai Guo-Qiang, known for his controlled explosion artworks and gunpowder paintings, as well as the special effects at the Beijing Olympics ceremonies. Chang Tsan-Tao and Ethan Wang supply the stunning lighting design and videography. The wind of the title is ever-present, as kites fly above the scene and big, gauzy flags flutter and parade as mobile screens for the projection of Cai’s fiery, smudgy pictures. Some of the dancers wear seven flags, harnessed to their bodies like wings, and look like archangels.

The shadow theme is also constant. As Lin’s choreography manipulates his black-clad “human” dancers in very slow, concentrated moves, others in full-body tights with obliterated faces become their floor-based shadows, duplicating the movements as if attached at the toes. But the shadows begin to take the lead, to break out and do their own thing. Then, as a group, they become a threatening tribe, or swarm and squirm like insects, simultaneously viewed in an angled mirror. This last is one of a few episodes that Lin draws out for far too long.

The soundtrack, which has often been quiet and distant, like music from outer space, is riven by escalating explosions and rattles like amplified gunfire, while Cai’s gunpowder blobs spatter across the white backdrop like tracer bullets impacting. We realise that what went before was the prelude to a cataclysm. The whole company slither in as the shadows, who now suggest burnt bodies, to be engulfed in a downpour of black snow and fire-tinged smoke while an astonishing whorl of light encircles a black hole. This light becomes a blade, which passes through each of us in the audience. It’s a powerfully apocalyptic spectacle. Then the 20 performers line up, face masks off, for the bows — smiling broadly, which is something they never got to do during the 80 intense minutes of the piece.

The dancers of Scottish Ballet have a great deal to smile about as they celebrate the company’s 40th anniversary this season. Their superb, purpose-built new headquarters opened recently at the Tramway international arts centre, in Glasgow, and they have won much acclaim since Ashley Page became director in 2002 and restored the adventurous spirit that used to be there in the formative, pioneering years under their founder-director, Peter Darrell.

The anniversary touring programme, which opened at Sadler’s Wells, is firmly of the present, as all three pieces have been acquired by Page. Balanchine’s Rubies, to Stravinsky’s jazzy Capriccio for Piano and Orchestra, is apt for the occasion and a wham-bam opener. With recent London performances by both the Royal and Mariinsky ballets in mind, however, there was a niggling feeling that Scottish didn’t come right up to the top with its technical demands. There was plenty of dash and zest, but something missing; though Sophie Martin and Adam Blyde did well with the fascinating pas de deux of curious moods.

Having scored a success with William Forsythe’s Artifact Suite, the company have followed up with his Workwithinwork, which they danced for the first time at this year’s Edinburgh Festival, and the result is compelling. Dancers come and go through dark holes in a distant void; the music is Berio’s Duetti, for two violins, recorded and chopped into segments so that the structure of Forsythe’s dance is episodic.

That tries the patience a little, but when the dancers move, it is a constant uplift, showing the chor­eo­­- grapher’s rock-solid classical base beneath every modernist construction. William Smith has a sort of focal function with a scatty flavour, while Paul Liburd and Tomomi Sato were especially admirable, but the whole cast of 16 impressed in a worthy acquisition.

In Light and Shadow, by the Polish choreographer Krzysztof Pastor, has proved a popular success for the company. The music is Bach, the Aria from Goldberg and Suite No 3, to which we have formal, courtly measures and lines a-leaping, a lot of fast entries and featured duets. Everybody is kept busy, with strong dashes of quirkiness. The blocked set is effective, but the mix of costumes — from little pants to baroque-esque flounces and skirts for men — is mad and distracting. The piece leaves me feeling uneasy, but the sinuous Daniel Davidson and others dance it to the hilt.

Editor's choice

• The 100 Best Films of the Decade
• 70 facts you didn't know about Marvel
• The 50 Biggest Movies Of 2010