Jeanne is 27, with a round face that makes her look younger, but she struggles on to the stage. She finds walking difficult, ever since she was tied to a tree and gang raped for many weeks, had surgery to repair the damage, went home and was raped again. She became pregnant during one of the attacks and was forced to give birth in the company of the militias; the baby died. Jeanne finally escaped to the Panzi hospital in Bukavu, at the eastern edge of the Democratic Republic of the Congo. She has had repeated operations on her desecrated lower body. She looks small, shy, defeated.

But then this woman, a victim of the biggest horror story of modern times, in one of Africa’s largest countries, steps up to the microphone and starts to speak.

“When you look at me, what do you see?” she asks, with the bold delivery of the born orator, the preacher, the leader. “Do you see me as an animal? Because you are letting animals treat me like one. You, the government, if it was your children, would you stop it? You, you white people: if this violence was happening in your country, would you end it?” She speaks with the kind of fury and focus rarely seen in western politics. Hundreds of other survivors of sexual violence in the audience cheer wildly.

Jeanne (who has requested her last name be withheld for her protection) is not the only speaker here at the opening of City of Joy, a centre for survivors of rape in Bukavu. There is the founder, the New York playwright, author of The Vagina Monologues and activist Eve Ensler. There is Obama’s ambassador for women and girls, a prominent congresswoman, someone from the UN. But it is Jeanne who steals the show. And this is the premise on which the centre is founded: that even the most traumatised and brutalised people need not be mere passive recipients of foreign aid, but can in fact become political leaders.

For more than a decade, eastern Congo has become infamous as the “rape capital of the world“ and the “worst place on earth to be a woman”. The UN has confirmed these facts. Half a million women, perhaps many more, have been raped since 1998, and in particularly brutal ways. And one response has been the building of City of Joy, a haven where survivors of gender violence who have healed physically (not always straightforward) live for six months and are educated. It is the product of a shared vision that the women don’t just need help, they need power. “Eve asked us what we wanted,” says Jeanne, the orator. “And we said: shelter. A roof. A place where we can be safe. And a place where we can be powerful. That’s what we now have.” Jeanne, and women like her, hope to change Congo for good.

Jeanne, 27: ‘If this was happening in your country, would you end it?’ Photograph: Paula Allen

The grand opening of City Of Joy, in February, is a big party: survivors in celebration clothes dance and sing and bang drums. Some, very badly injured, are carried in. Women who helped construct City of Joy dance with bricks balanced on their heads. Local men taking a stand against sexual violence – the “V-men” (after Ensler’s feminist V-Day movement) – make themselves visible with special T-shirts. American donors join a conga line. Women from the stage speak not just of rape but about laws that discriminate against women, the lack of free HIV treatment, what happens to the children of rape. There’s a lot of hugging, but the atmosphere is fierce.

The centre’s story begins in 1999, when the gynaecologist Denis Mukwege, of Bukavu’s Panzi hospital, rang his friend Christine Schuler-Deschryver, a human rights worker in the town. He said he had started to see injuries he had never seen before – women who had been raped in terrible ways, whose reproductive organs had been wrecked, who were suffering from fistulas between the vagina and rectum inflicted not just by gang rape but also by attacks with sticks, guns, bottles. “I said to Christine, this is new,” he recalls. “Their vaginas are destroyed. I couldn’t understand what was going on.”

Everyone in Bukavu knows Christine – she is 6ft without heels (and she’s never without heels), mixed race (her father was from a family of Belgian colonisers, her mother a Congolese servant in the tea fields of his plantation), dramatic, demanding. “When Dr Mukwege told me about these injuries, we were very afraid,” she says. “And then, in 2000, I was in my office when a woman ran in with a baby girl, 18 months old, her legs both broken back – the baby had been raped. She died in my car on the way to Panzi hospital. I ran into the cathedral with the dead baby in my arms, shouting at God. And that was the day I became a radical fighter.”

Left to right: City of Joy founders Eve Ensler, Denis Mukwege and Christine Schuler-Deschryver. Photograph: Paula Allen

Bukavu is a ragged, devastated town built on the banks of Lake Kivu in the east of Congo; at one time the Belgian colonisers tried to make it a lakeside retreat, so stunning is the setting. There are no roads, so when it rains the pathways turn to mud. Women (rarely men) stagger beneath gigantic sacks of cassava and charcoal; they sit on the ground with a single tomato to sell. Once a town of 50,000, it is now home to hundreds of thousands, most of whom have fled fighting in the bush to come to the comparative safety of the city.

Congo is the size of all of western Europe, with a very weak state. It is also the poorest country on earth, by GDP, and yet one of the richest in terms of resources – the fertile soil that produces such a lush landscape and juicy avocados brings with it gold, diamonds and precious minerals, with criminals, militia and kleptocrat politicians not far behind. Since colonialism, when King Leopold II of Belgium ran a notoriously genocidal regime in order to plunder Congo’s rubber, armies have tried to grab its wealth. President Mobutu, who renamed Congo Zaire and stole a personal fortune of billions, showed that it wasn’t only outsiders who could get in on the act. Today’s gold rush is over coltan – Congo has 80% of Africa’s reserves of the mineral, which is used in mobile phones, laptops, iPads; with the resource in such demand, there’s a direct link between the technology consumer boom and the fighting in Congo.

Rape is a feature of war, and is often seen as an inevitability – the second world war general George Patton wrote that “there would unquestionably be some raping”. But it is more widespread and more violent in some wars than others. According to Joanna Bourke, author of Rape: A History, its prevalence depends on how violent a society is already; the disparities between men and women in the culture; whether soldiers fear any kind of punishment for rape; and the extent to which the values that enable mass rape are shared by men on each side of the conflict. On every count, Congo rates disastrously. And there’s also a particular problem, what Jean-Claude Kibala, the deputy governor of South Kivu, describes as a “bomb in the middle of society”: former child soldiers. “Nobody has a programme for how to deal with them,” he says. He tells of a bodyguard who kept falling asleep during the day. “The bodyguard explained, ‘When I was a child I was forced to bury a man who was still alive. This image is with me every night and I can’t sleep in darkness.’ There are people like that all through our society. Destruction and rape are destroying all humanity in the province.”

The particular brand of brutality that emerged in eastern Congo in the late 1990s has its roots in the Rwandan genocide of 1994, when 800,000 Tutsis and some Hutus were murdered in three months by Hutu gangs known as the interahamwe (what they call themselves) or genocidaires (what their opponents call them). When the genocide was stopped by the arrival of the Tutsi exile-led Rwandan Patriotic Front, the interahamwe fled to eastern Congo where they established gigantic refugee camps in Goma, a town close to the Rwandan border. Notoriously, the global aid community responded to the refugee crisis with an efficiency that was missing from the response to the mass slaughter of the Tutsis: they fed, clothed and inoculated the genocidaires and their followers, while the few Tutsi survivors mourned their families and scrabbled around for food. The interahamwe who did not take up Rwandan president Paul Kagame‘s offer to return home disappeared into the Congolese bush.

The Rwandan genocide was, in the words of French writer Jean Hatzfeld, “enthusiastic processions of ordinary people who every day went singing off to work as killers”. Neighbours and friends went out “hunting” Tutsis with farming implements such as machetes and hoes. But it wasn’t straightforward murder. As interahamwe leader Adalbert Munzigura told Hatzfeld in A Time For Machetes: “They needed intoxication, like someone who calls louder and louder for a bottle. Animal death no longer gave them satisfaction, they felt frustrated when they simply struck down a Tutsi. They wanted seething excitement. They felt cheated when a Tutsi died without a word. Which is why they no longer struck at the mortal parts, wishing to savour the blows and relish the screams.”

It was these very interahamwe who imposed themselves on the Congolese people, later reinvented as a militia called the FDLR (Forces Démocratiques de Libération du Rwanda). And over more than a decade of violence, in which power passed from Laurent Kabila to his son Joseph, Rwanda invaded Congo, there was Africa’s “first world war”, which was played out in Congo (involving Uganda, Rwanda, Burundi, Zimbabwe, Angola, Chad, Namibia and Sudan, and leaving an estimated 5.4 million dead, according to the International Rescue Committee); through all of this, a multitude of new and primarily Congolese rebel militias were formed, and all of them raped women with extreme violence. Which is why Dr Mukwege started to see injuries he’d never seen before.

Rape, devastating everywhere, particularly undermines Congolese society. After being raped a woman is usually excluded by her family and so, when women have the babies and do all the cooking, farming, carrying, community is quickly undermined. Society breaks down. “If you destroy women, you destroy the Congo,” Ensler says. “Raping women is the cheapest and most effective way to instil fear in and humiliate a community. It doesn’t even cost a bullet.”

But is there something deeper at work? Has the epidemic mass rape in Congo got something to do with the country’s own history, the result of many years of subjugation, played back? Michela Wrong in her book In The Footsteps Of Mr Kurtz memorably describes Congo’s population as being “marinated in humiliation”. Says Ensler: “There is so much rape in men who’ve been colonised and enslaved. You have to wonder what it’s done to these men, to their collective psychological memory.” The Belgian colonists were famous for cutting off hands and feet, still a common rebel tactic – Jeanne was forced to watch as her uncle’s hands and feet were cut off before he was murdered. Says Ensler: “Centuries of colonialism, slavery and exploitation by the west have come together and are now being delivered on the bodies of the Congolese, most dramatically on the bodies of women.”

The particularly violent way of rape that has become current destroys the women’s reproductive organs. They can no longer have children (especially terrible in a society in which motherhood so defines being female that the word for “woman” is “mama”). As Mukwege, who has worked for more than two decades with women on the ground in eastern Congo, says, “This will be the destruction of the Congolese people. If you destroy enough wombs, there will be no children. So then you come right in and take the minerals.” Here in Congo, in the heart of Africa, home of the origin of man, the rapist wants to stop the human race for good. I was told of a woman being raped who asked the rapist why he was doing it. He replied, “Because I’m already dead.” Not for nothing does Ensler describe Congo as “ground zero”.

The raped women I spoke to have a straightforward request for how to solve the problem of rape in Congo: get the FDLR (the genocidaires and their descendants) out of the country. A common Congolese refrain is that “rape is not in our culture” – ie, foreign warlords brought it with them – and certainly, returning the FDLR to Rwanda would be a start, as would Rwanda taking responsibility for the other militias in the area it supports.

But it is now much more widespread: brutalised mass rape has become so endemic that the Congolese army, much more populous than the FDLR, reportedly commits most of the attacks. Rape has become normalised – and is only one, dramatic, dimension of a far wider violence taking place throughout the region. “Rape in Congo has tended to attract the headlines,” says Carina Tertsakian of Human Rights Watch. “There are also other serious abuses: killings of civilians, arbitrary arrests and widespread looting are all commonplace.”

But something is changing. In February, lieutenant colonel Kibibi Mutware and three other Congolese army officers were convicted of crimes against humanity for ordering rape and other crimes in Fizi town, South Kivu, on New Year’s Day this year. They were sentenced to 20 years in prison. This is truly a landmark – the first time a senior ranking Congolese army officer has been arrested, tried and convicted for rape crimes. But one case is hardly enough: there has been no action taken against other officers accused of similar crimes also committed that same day, the mass rape of 39 women and one girl in Bushani and Kalambiro villages in North Kivu. And, as Ensler asks: “Will they keep the lieutenant colonel in jail?” But it is, at least, something.

The women of Congo have been hopeful before. Since the late 90s, they have been intermittently fashionable as a global cause in the west; an activist wryly noted that every 18 months or so there’s a flurry of media interest, gruesome rape stories are related, each more terrible than the last, and then there’s silence. “They come and visit,” Schuler-Deschryver says bitterly, “and leave me with a pile of business cards.” Hillary Clinton, the US secretary of state, visited in 2009. “I made Hillary cry when she came, and it made me full of hope. But then – nothing.”

Melanne Verveer, who, in a new role created by Obama, is the US ambassador for women and girls, and who attended the opening of City of Joy, denies that the Clinton visit was followed by no extra money; her aides fluster around me proffering sheets of numbers, proclaiming cash provided ($42m over five years, they say). But Congo is clearly not a priority for international aid: when Ensler went to talk to Michelle Obama about the cause, she got inside the White House before an aide, high up in the Obama administration, informed her that “Congo was not going to be part of the Michelle brand”. It is notable that, despite the enormous hope raised in Africa when Obama was elected, both his predecessors, George W Bush and Bill Clinton, showed more interest in the continent.

Although the money for City of Joy is provided by Ensler’s movement V-Day (which raises cash through performances of The Vagina Monologues), plus Unicef and various foundations and donors, all are keen to emphasise that the project is owned and led by Congolese women. And their big idea is not aid, but empowerment. If we accept that rape is a violent expression of the power imbalance between men and women, then you prevent rape by helping women get more power. In other words, the City of Joy is all about a Congolese kind of feminism.

The programme will be run by Bahati Bachu, a strong-looking woman who carries an air of disbelief that this City of Joy is happening at all, and is a living, breathing rebuttal to those who imagine that feminism does not exist in developing countries. She is 58 (a good age in Congo, where life expectancy is 53) and a longtime women’s rights activist, a tough role to take in this harsh place. For international women’s day in 1999, she asked all the women in Bukavu to stay indoors; they did, and the entire town shut down. She was sacked from her role as regional women’s officer as a result. She once threatened to walk bare-breasted through the streets as a protest against women’s place in society. “When the rapes started to happen, I denounced it everywhere,” she says. “Germany, France. And nothing. I worked for so many years for Congolese women, but eventually I stopped because I was discouraged. But now, with City of Joy, I am seeing the fruit of my work, and others want to join. I will not die before we have a revolution.” She does not laugh at this.

Mama Bachu’s programme lasts six months. Survivors have “de-traumatisation” sessions; they learn about women’s rights (“Some are shocked to hear they have any rights at all,” Bachu says), literacy, the economy, accounting, farming, production, business, self-defence, the internet. (Google has donated a £100k technology centre.) Says Schuler-Deschryver, “Everything is Congolese, not American. So there’s no therapy, talking about your relationship with your father.” The women asked for small brick houses, arranged like a village, and a place for exercise, “so we can use up our energy and not row in the evenings”.

Sixty women will live here for six months, passed on from the gynaecology ward at Panzi hospital, after Dr Mukwege has saved their lives. They come from all over Congo. As the Congolese ambassador to the US, Faudi Mitfu, says, “City of Joy shows that even when a woman has been terribly tortured, she can still stand and build.” And, perhaps more hopefully: “Today we build City of Joy. Tomorrow we build our country.”

It’s almost unbelievable that the poorest country on earth could give birth to a women’s movement, just like the incongruousness of the beautiful landscape with the horrific past and present; the terrible damaged lives with the singing and dancing. It’s got to have a chance. As Schuler-Deschryver says, “There’s something you need to know about Congolese women. When we can’t walk, we run.”

• Read Katharine Viner’s books blog on this story.