"I want to protect and develop the Bolshoi's unique style," says Alexei Ratmansky, the new director of the great Moscow company. "And I want as many new productions as possible." The Bolshoi Ballet is in Covent Garden for three weeks, its first full season here for five years. It has been a time of drastic upheaval for the company.

Since the end of the Soviet Union, the Bolshoi has been seeking a new identity. The Soviet-era Bolshoi was shaped by the director-choreographer Yuri Grigorovich, who ran the company for 30 years. Since Grigorovich left, in 1995, the theatre has struggled with artistic, funding and management crises: Ratmansky is the company's fourth artistic director in less than a decade.

Ratmansky, a 35-year-old choreographer, is certainly a change for the company. He trained at the Bolshoi school, but has never danced with the company. He has spent most of his career in the West, recently with the Royal Danish Ballet, and this is the first time he has directed any company. He even had to take Russian citizenship before he could take up his new post since, although he was born in St Petersburg, he held a Ukrainian passport. He is frank but diplomatic. He praises the company's great history while pointing out things he wants to change. His main concern is broadening the Bolshoi's repertoire. "This is a brilliant company, full of young, talented people. Yes, it's inspiring to be able to perform the classics, and we have all the classics. We should also be giving these dancers the opportunity to develop their talents, to give them new roles, different styles, the chance to work with choreographers. This was missing for a long time."

The repertory for the Bolshoi's London season shows a company in transition. Grigorovich is still there, represented by his Spartacus and his production of Swan Lake. There's also Fadeyechev's well-liked production of Don Quixote, which opened the season on Monday. You can see the Bolshoi's recent search for direction in two new ballets. The Pharaoh's Daughter is an extravagant spectacle, modelled on the grand ballets of the 19th century. Romeo and Juliet, which had its premiere last year, is a modern dance production staged by the British theatre director Declan Donnellan.

This Romeo... is the Bolshoi without pointe shoes. "It was something new for us," explains the young ballerina Maria Alexandrova, who was the Juliet in the first cast. "Though for the rest of the world," she adds, "probably it was already in the past. Modern choreography has already been mastered in the west, but for us, we still have to find our way to approach it."

Unusually, this is a ballet staged by a theatre director. Donnellan, founder-director of the British theatre group Cheek by Jowl, is much admired in Russia. At first, the Bolshoi Theatre invited him to direct an opera; doing a ballet was his own idea. The concept is Donnellan's, but he needed help with the technicalities of dance, and turned to the Moldovan choreographer Radu Poklitaru. There hasn't been much praise for Poklitaru's choreography, but this Romeo... has been welcomed as a new departure, a different challenge for the dancers. "In the classical ballets, it's like behaving in polite society," Alexandrova explains. "You have to produce your good manners, to keep all your skeletons in the closet. In modern dance, you just reveal everything that you have." She adds: "You have to be ready for it. Sometimes you wake up in the morning and think: 'I'm not much Juliet today,' but you have to go through that. It's a great joy to show that you have these emotions."

The Bolshoi go from their stark modern Romeo... to the opulence of The Pharaoh's Daughter, created in 2000. This an entirely new ballet, though its plot and music were created almost 150 years ago. The 1861 Pharaoh's Daughter was the first big Russian ballet by Marius Petipa, the great choreographer who went on to create The Sleeping Beauty and La Bayadere. Even by the standards of 19th-century ballet spectacle, the plot is lavishly, sumptuously silly. Recent excavations had made Egypt fashionable, and Petipa's production made the most of it. His ballet opened with English explorers, who take refuge from a storm by hiding in a pyramid. Once inside, the hero smokes opium, and the whole ballet unfolds as an Ancient Egyptian dream sequence. There's a real horse, a fake lion, a divertissement danced at the bottom of the Nile.

Right now, the reconstruction of early productions is in fashion but this Pharaoh's Daughter is a different approach. The French choreographer Pierre Lacotte has bypassed the 19th-century notation, choosing to make new steps "in the manner of" Petipa. A description of Lacotte's choreography doesn't actually sound much like Petipa. The spectacle is certainly there, but he has cut down on mime scenes and beefed up the male roles. His dances are full of steps popular in pre-Petipa Romantic ballets, with lots of quick, detailed footwork.

"It's a very good school for our dancers," says Ratmansky. "It gives them batterie [steps where the dancer's legs beat together], little transitions between the big steps. They haven't always paid attention to those, because they're trained in the choreography of Grigorovich, which is very big and dynamic."

The Pharaoh's Daughter was immediately popular but struggled to stay in the repertoire as Gennadi Rozhdestvensky, then the Bolshoi's chief conductor, objected to the rum-ti-tum score by Cesare Pugni. But audiences clamoured for it, and it returned in triumph.

Whatever they learn from The Pharaoh's Daughter, the Bolshoi is still known for the grand scale of its dancing. The Bolshoi Theatre itself, with its vast stage, encourages strong projection from the dancers. "When you stand on our stage, you have a huge space in front of you," says Alexandrova. "You know the audience is there, it's waiting. But there is some obstacle you have to overcome to reach them - you have to cut this space between you." The Bolshoi Theatre, now almost 150 years old, will soon close for redevelopment. Instead, the company will be dancing on the smaller New Stage. Until now, this 1,000-seat theatre has been used for experimental work, including the Donnellan Romeo.... When the Bolshoi Theatre reopens, the real challenge will be finding new ballets that can survive its huge auditorium. "Some productions lose something on our stage," admits Alexandrova, "it swallows them."

That scale is part of the Grigorovich ballets, and it's one reason why they're still popular. "Spartacus and Legend of Love are very important ballets for the Bolshoi," says Ratmansky. "They're in very good shape, we have good dancers to perform them. Spartacus in particular shows the male corps at their best." Alexandrova, who will be dancing in Spartacus in London, agrees. "You can't just delete this out of our repertoire, because these are such great ballets," she says. "If you have a diamond in your collection, you don't throw it out."