The Bolshoi Ballet is back with a dynamic artistic director and exciting new productions

Last year, it suddenly became clear that there was a lot of good news about the Bolshoi Ballet. Visiting London for a summer season, the Moscow company looked revitalised, with exuberant performances from young soloists as well as principals. Then there were two stellar events. First, the Bolshoi's young artistic director Alexei Ratmansky showed his own ballet The Bright Stream, an irresistible romp with a Shostakovich score. Then the 2006 visit ended with a bang, when the 20-year-old Natalia Osipova made her debut in Don Quixote – a star-is-born performance, with Osipova showing sensational technique and fizzing stage presence. Critics and fans gathered in happy huddles in the foyers. The Bolshoi was back on top of the world.

A major company in full flight is always exciting. As the Bolshoi comes to the Coliseum for another London summer, it brings a sense of renaissance. This current success is a recovery, a return to form after a painful period of adjustment. Since the end of the Soviet Union, the company has faced and survived funding, artistic and management crises. Ratmansky's Bolshoi has both a new strength and a new sense of its own past.

Under communism, the Moscow company was a flagship of Soviet culture, lavishly supported by the state. When the Bolshoi first appeared in the West, in 1956, the sheer scale and power of the dancing caused a sensation. Bolshoi technique – particularly the high, spectacular lifts – and Bolshoi characterisation had a huge impact on companies around the world.

By the 1990s, the company's position was crumbling. With the end of the Soviet Union, Russia's great ballet companies lost their financial security. They also lost dancers, with many heading west in search of better fees and easier living conditions. The Bolshoi took the change hard. There was a quick turnover of artistic directors, and different attempts to find a new identity. Western tours took on a desperate edge. In 1996, there was even a disastrous Las Vegas season, with the Bolshoi playing to sparse audiences of gamblers.

With the new millennium, the company began to recover. Ratmansky, who took over in 2004, has been careful to share the credit for the Bolshoi's revival, praising his predecessors' work. His own appointment came as a surprise. He was young, born in 1968, and came from outside the company. Having trained in Russia, Ratmansky went west, dancing with the Royal Danish Ballet. The Danish style is pretty much the opposite of the huge, high-octane Bolshoi: fleet and buoyant, with a naturalistic sense of drama. In the past three years, Ratmansky has tried to add those qualities to the Bolshoi style, demanding speedy footwork alongside a huge sense of scale.

That scale is part of the company's identity. It's the effect of its home stage, the Bolshoi theatre in Moscow. Bolshoi means "big", and dancers have to project powerfully to be seen in that huge space. The theatre closed for refurbishment in 2005 and is due to re-open in 2008. In the meantime, most of the company's Moscow performances take place on the smaller New Stage.

If the end of Soviet communism brought financial insecurity, it also brought greater artistic freedom. Russia's two leading ballet companies, the Bolshoi and the Mariinsky (formerly the Kirov) have brought in repertory from the West, staging 20th-century classics and commissioning new works. The Bolshoi's brushes with Western choreographers have been mixed: there was an awful Romeo and Juliet by the British theatre director Declan Donnellan and a scenery-chewing Queen of Spades by the French choreographer Roland Petit.

This year, the Bolshoi have staged a new work by Christopher Wheeldon, the golden boy of Western ballet. Elsinore, a Hamlet ballet danced to Arvo Part's Third Symphony, started out under the title Misericord, since Wheeldon was reluctant to stress the ballet's Shakespearean background. Since the successful Moscow premiere, the title has changed to Elsinore, an acknowledgement of the Hamlet theme.

There's another import in this London season. The Cuban Carlos Acosta, one of the most celebrated male dancers of his generation, will be the first Westerner to dance Spartacus, by the former Bolshoi director Yuri Grigorovich. This slaves-and-gladiators ballet is a huge, crude epic. It's not subtle, but it shows off the Bolshoi's capacity for large-scale sincerity.

In recent years, the company has had a shifting relationship with this signature work. When Grigorovich was in charge – he was the director from 1964-1995 – he groomed male dancers who could dance his massive choreography, beefy heroes such as Irek Mukhamedov. Since Grigorovich's departure, Bolshoi men have changed, becoming leaner and quicker. Ratmansky has said that Grigorovich's works will be kept in the Bolshoi's repertory, but he doesn't come across as a fan. The invitation to Acosta is fascinating, because it's a different approach to an inescapable ballet. Acosta gets a technically demanding role, a breakthrough in relations between the Bolshoi and the West. Ratmansky gets a new take of Spartacus.

Acosta is an established star in London. But the most eagerly-awaited male dancer is Ivan Vasiliev. At 18, Vasiliev has generated a buzz, already known for high, bold jumps and crisp, speedy turns. In London, he is scheduled to dance Don Quixote with Osipova.

When Ratmansky took over the Bolshoi, he was building a reputation as a choreographer. As director, he has made few ballets for the company, just three out of 20 new commissions. He has also been producing as well as choreographing ballets. For Le Corsaire, the new production that will open the London season, he does both.

Le Corsaire has a long, complicated history. Based on a poem by Lord Byron, this tale of pirates and harem girls was staged as a ballet in Paris in 1856. Two years later, it was re-staged in Russia, this time with an interpolated dance by Petipa – the choreographer who went on to create The Sleeping Beauty. Over several decades, the ballet was staged and re-staged.

In one sense, the new Corsaire, produced by Ratmansky with Yuri Burlaka, is part of a trend for "authentic" stagings of 19th-century ballets, such as the Mariinsky's recent reconstructions of The Sleeping Beauty. Le Corsaire has been revised so often that authenticity just isn't possible. Instead, Ratmansky and Burlaka are aiming to create a new composite version.

They're keeping as much Petipa as possible: some dances are still in repertory, others are reconstructed from 19th-century notation. Later alterations have been kept, too. The Corsaire pas de deux, a famous gala showstopper, started out life as a pas de trois for the heroine, her lover and a devoted slave. In the Ratmansky/ Burlaka version, it's back to being a pas de deux. Then there's the new material. Where dances have been lost, Ratmansky has created his own dances. Reports from Moscow suggest that the new Corsaire is lavish, stuffed with new dances. Ratmansky's inventions have been praised.

Looking back to the 19th century is another way of rethinking the Bolshoi's present. Though it has always kept the 19th-century classics, the Bolshoi's productions have substantially changed the old ballets. The company is still stuck with Yuri Grigorovich's ghastly Swan Lake, but Ratmansky is adjusting the Bolshoi's classical identity.

Reconstruction is also part of his own identity as a choreographer. The Bright Stream, the ballet that has been most popular with Western audiences, is another new version of an old ballet. Shostakovich's 1935 score, depicting happy life on a collective farm, was first choreographed by Fedor Lopukhov, then banned by Stalin.

Ratmansky's version, created in 2003, went back to Lopukhov's story and setting, creating a gleeful new ballet. Boris Messerer's designs were wildly colourful. The plot bubbled over with complicated intrigues, while the dancers raced through quick, detailed steps. Critics and audiences were enchanted across the world.

If The Bright Stream is a delight, it's also a surprise. Ratmansky went back to the 1930s, back to a grim time in Russian history, and created a romp. Messerer's frontcloth showed quotations from newspaper articles, including attacks on Shostakovich and the first version of this ballet. Yet the ballet's depiction of a collective farm has an exuberant innocence, a celebration of the world as it might have been. This isn't kitsch, or irony; Ratmansky takes on Lopukhov's story with whole-hearted enthusiasm. As the Bolshoi recovers from a decade of upheaval, the company is looking both back and forward.

Bolshoi season, London Coliseum WC2 (0870 145 0200) 30 July to 18 August