It was a remarkable victory when the social networking giant Facebook caved in to pressure last week and promised to "do better" to tackle anti-women hate pages on its site. A campaign by three women succeeded where many previous efforts had failed, forcing Facebook to take action over content celebrating rape and domestic violence.

It took just a week for the campaigners to rouse hundreds of thousands of supporters, thanks to a growing digital network of women who are part of the "great feminist revival". Spare Rib magazine is soon to relaunch, women's groups are enjoying a growth in interest, and online feminism is flourishing in blogs and tweets. Beyoncé and Madonna were in London for the Chime for Change concert, promoting global empowerment for women and girls.

The F-word is back, with digital-savvy young women joining forces online. Here the Observer selects some of the best voices in activism.

Kat Banyard, 30, author and co-founder of UK Feminista

Kat Banyard. Photograph: Frantzesco Kangaris

The campaign group is especially concerned with the commercial sex industry and work to close down lap-dancing clubs.

"The scale on which women are now sexually objectified means feminists today are in uncharted territory," says Banyard. "In the 70s and 80s they didn't have what we have now: developments in technology and a concerted PR campaign that has enabled sexual exploitation to become a global industry. The result is misogynistic, violent, online pornography, lap-dancing clubs in the high street, lads' mags on display in supermarkets. It's deeply ingraining a cultural message that it's acceptable to dehumanise women, to treat women like sex objects. What we are now seeing is a resurgence of grassroots feminist activism, with people of all ages mobilising online and on the streets because they want an end to the sexism that is still rampant in our society."

Lucy-Anne Holmes, 36, novelist and actor

Holmes became a feminist heroine after starting an online petition at Change.org calling on the Sun editor, Dominic Mohan, to stop using page 3 topless models. It has attracted more than 100,000 signatures and the support of the Girl Guides.

"We are asking very nicely: stop showing topless pictures of young women … stop conditioning your readers to view women as sex objects," she says. "I felt strongly that when the largest female image in the most widely read newspaper in the country is a young woman in her knickers, there for men to look at, it doesn't send out a respectful message about a woman's place in society. It says: 'What society values about you first and foremost is how sexy men find you in your pants when you're about 20."

Caitlin Moran, 38, newspaper columnist, TV critic and prolific tweeter

Caitlin Moran. Photograph: IBL/Rex Features

Moran has built up a huge following for witty writing that attacks everyday discrimination, from Disney's sexualisation of its princesses to nudity in pop videos. She has also stirred up controversy among some feminists, who find her too flippant.

"When women say: 'I'm not a feminist,' well, you have to be, you are," she said in an interview. "Unless you've gone and handed back your vote to parliament or wherever, all women in the first world are feminist by default. You're seen as a free agent, your paycheque goes into your bank. Unless you've gone and undone those feminist opportunities, you just are. We're post-wave. There are very few men and women in the first world who aren't feminists; they just don't know what the word is.

"This isn't a failure of academic feminism; it's just that popular culture dropped the ball. We stopped having reference points in pop, in movies – you can jokingly blame it on the Spice Girls, but before that it was grunge, and girls didn't wear makeup and got on with what they wanted to do. Now Adele is the first woman in 16 years who has an arse and wears sleeves and gets to number one."

Laura Bates, 26, founder of the Everyday Sexism project

Laura Bates. Photograph: Ken McKay / Rex Features

Bates set up everydaysexism.com last year and it has since had 30,000 incidents reported by women and children. She co-founded the #FBrape campaign and won an unprecedented vow from Facebook to act over gender-hate content on its site.

"The internet allows you to find such strong support," she says. Everydaysexism.com has become enormously popular because women get so used to street harassment and sexism that it's become normalised and you're seen as uptight if you draw attention to it.

"It has a cathartic effect for women who can relate their experiences of sexism without the usual 'oh, I think you must have got the wrong end of the stick there' or the 'making a lot of fuss about nothing' type responses, which is so common.

"It's really striking how the same themes come up whether you're a woman working in a burger bar, a woman in the City, a woman in a wheelchair, even a girl in her school uniform. And having all these experiences in the same place is proving useful to policymakers. I've had MPs working at the info and we're working on a project with the police, so I'm proud that women's real experiences are being heard."

Laurie Penny, 26, author, feminist, socialist and columnist

Laurie Penny. Photograph: Ken McKay / Rex Features

She blogs and tweets under the name Penny Red and is now a contributing editor at the New Statesman.

"There is a lot of fighting out there at the moment within feminism over what it is and what it should be, and it's exhausting but necessary. It's part of the process," she says.

"There are a lot of people who think either populist feminism or the other extreme is nonsensical, who want to demean sex workers or to protect their rights, and what the internet means is that we can't ignore each other. It also means people are a lot more educated than they were in the 60s and 70s when consciousness was about finding each other; the internet makes that faster.

"Sexism is becoming more apparent to girls at an ever younger age. The sexual violence in schools is astonishing and the internet is making that more apparent. But feminists have a way of coming together on the big issues."

Yasmeen Hassan, global director of Equality Now

Yasmeen Hassan. Photograph: Dimitrios Kambouris/WireImage for Equality Now

Equality Now is one of the groups behind the Chime for Change concert in London, a campaign for empowerment of women and girls.

"The conversation in this country and the resurgence of feminism is wonderful," she says. "It's so encouraging to see these conversations happening, especially as in America it is still a forbidden, bad word. Too many young women there will say 'oh, I'm not a feminist', when in fact if you talk to them and unpick that, of course they are. Theidea of liberation in America is more sexual and here it is much more intellectual, but the internet is opening up channels between women in different countries, and women who might be isolated in their communities, to understand each others' lives and support each other, which is the heart of feminism to me. We need equality to make our societies better for both men and women."

Nimko Ali, 29, is a feminist blogger and co-founder of the Daughters of Eve

Nimko Ali. Photograph: UK Sexual Health Awards

Around 30,000 girls in the UK are at risk of suffering the illegal practice of female genital mutilation. Ali, at 7,was a victim of FGM when her mother took her to Somalia.

"My FGM was out of context in that I grew up in a feminist family. I knew FGM was wrong and assumed everyone else would. Sadly, this wasn't so and I understood my own silence was complicit in this. As a form of violence against women, FGM takes place because of structural inequalities in society – particularly gender inequality," she says. "We need to empower and protect those at risk to make sure that it is eliminated. Any approach to end FGM which does not address these inequalities will only leave a vacuum for another form of violence against women – or for those who carry out FGM to say that it does not exist. Progress is definitely being made. In Bristol, we have hundreds of young people who are not only standing up and speaking out about FGM, but questioning the role of women within their communities. They are being empowered with language that has not just changed their lives, but also those of their mothers. As one woman said: 'If it is OK to cut a girl because she is a girl, then what you will do to her as a woman will be worse.' This change has not come easily for those of us that have stood up against FGM. We face death threats on a regular basis, we have been attacked on the street and lost people we once believed to be friends."

Lili Evans, 15, is one of the women behind the Twitter Youth Feminist Army

Lili Evans. Photograph: Lili Evans

Bloggers and young activists are finding each other under the Twitter hashtag TYFA. Lili also has a blog with a friend (jellyandlilipop.wordpress.com) which connects young feminists, and she has started a feminist group at her school.

"I guess I became a feminist when I actually looked at the world and saw how unfair it was," she says. "Women. People of colour. LGBT people, who have much harder lives for no good reason. I set up the Twitter Young Feminist Army with two other girls who are sadly no longer on Twitter because of the misogynist abuse directed at them. But mostly there's a great community online. Quite a lot of young girls are isolated, maybe their friends aren't interested in feminism and they are a bit scared of joining groups of older women, so we help them connect. At our age you get told not to wear short skirts to school and then you get shouted at by men in cars on the way home anyway, and realising that it's wrong and that there are other people out there who share your views is great. The thing I'd really like to see happen is equal pay, and access to better sex education and contraception advice for younger people."