A few years ago, someone had the bright idea of designing a T-shirt with the slogan "This is What a Feminist Looks Like" running proudly across the chest. The Feminist Majority Foundation, selling them online, reported a run of orders from college campuses across America. In the UK, equality champions the Fawcett Society plugged the T-shirt on their website, asked prominent faces – from Tracey Emin to Ken Livingstone – to wear it in public, and it became a bestseller. Then, last year, Ms, the American feminist magazine, put Barack Obama on its January cover. There he was, a shiny illustration of a President, chin uplifted, staring heroically into the middle distance, ripping his white shirt open, Superman-style, to reveal that T-shirt.

The point? Feminists come in all shapes, sizes and sexes. The Undomestic Goddess blog has set up a website, Thisiswhatafeministlookslike.tumblr.com, where people can post snapshots of themselves, sitting at their desks, walking their dogs, wearing their wedding dresses, living their lives – feminists one and all. It's a superficial point they're making but if, like me, you grew up in the Eighties, it's an important one. We children of Thatcher have a fairly confused idea of what a feminist looks like. For the first nine years of my life, we had a female, but not feminist, prime minister. ("I owe nothing to women's lib," said Maggie. Thanks sister!) If there was a woman at No 10, the war was over wasn't it? As I was growing up, women were battling their way into every male-dominated walk of life, from the armed forces to the boardroom and even the church, but the only feminist I remember seeing on television was Jo Brand, and she never looked terribly happy about it. I was too young to know anything about the riot grrrl punk movement in America, other than the story of one of them (Donita Sparks from L7) tossing her used tampon into the mosh pit at the Reading Festival, which made feminism seem a bit gross. As I was taking my GCSEs, the Spice Girls took up the feminist mantle, though they called it "Girl Power" to make it sound a bit more fun. And as I was studying for my degree the Sex and the City girls and Jordan stripped off, had plastic surgery, boasted about their bedroom exploits and decided they were feminists too.

Confusing – and none of it very convincing. Perhaps Germaine Greer could help? When I was 19 years old, she came to speak at my university. I went, a little sceptically, to see this curious much impersonated, wild-haired Antipodean rent-a-quote in a grey kaftan. Knocking the Union committee off their self-important perches, swatting away impertinent questions from posh public school boys who thought they were funny, swearing indiscriminately and using the C-word, liberally, in a way I'd never heard before, she was heroic. I resolved to read The Female Eunuch immediately. Being a student with Crime and Punishment to read by Thursday, I did no such thing. Still, it was a thrilling glimpse of a real-live feminist firebrand.

But then she went and confused matters again. Her appearance on Celebrity Big Brother in 2005 – wading through manure with a colander on her head, riding a roundabout until she vomited and trying vainly to rouse her housemates to a naked sit-down protest before leaving in a blaze of righteous anger blasting the show for being a bullying, immature bear pit for publicity-hungry has-beens (like, dur...Germaine) – felt very wrong. Since then there have been controversial rants about everything from female circumcision to Steve Irwin, cameos on Extras and a slightly odd book about the allure of adolescent boys. Somewhere along the line, her clarion call for female emancipation got lost.

Now is the moment to find it again. This year marks the 40th anniversary of The Female Eunuch. When it was first published in 1970, the passionate polemic calling for the end of the oppression of women caused a sensation. Edward Candy, in The Times, called it a "frightening book" which was "likely to set fastidious teeth on edge". Sally Kempton, reviewing it for The New York Times, approached it "with suspicion" after no fewer than four men recommended it to her, but was relieved to find it "brilliantly written, quirky and sensible, full of bile and insight". Norman Mailer, in the infamous New York City Hall debate on feminism, dismissed Greer as a "lady writer" and her views as "diaper Marxism"– whatever that means. The sales racked up. The book hit the bookshelves in October of 1970. By the following March it had nearly sold out its second print run and had been translated into 11 languages. It made Greer rich – $29,000 for theUS rights and a further $135,000 for the paperback edition from Bantam – and a household name.

And all the while, women were reading it, passing it around the university common rooms, for sure, but also devouring it at home. Some wrapped its surreal, bracing cover (the limp skin of a bare-breasted torso hanging from a rail) in brown paper and hid their copy among the shoes in the bottom of the wardrobe like furtive Libo-holics. Others, emboldened by its message, hurled copies at their husbands' heads over dinner. Needless to say, more women read it than men. My mother remembers distinctly going out to buy it as a newly married woman in 1970, and the stir it created. Does my father remember anything similar? "No, not much", he says. "Why would I?" Good point.

That was then. But how does The Female Eunuch stand up in 2010? Does it still have the power to shock, thrill and mobilise that it had in 1970? Is Greer still germane? I decided to find out. I was vaguely ashamed that I had reached the age of 28 without reading it. I asked around my friends; most of them hadn't read it either. "I don't need to", said one. The few that had – including a solitary, enthusiastic, male (his wife made him read it) – lit up when I mentioned it, delighted to welcome a newcomer to their cult. The book's mystique – that title! What does it mean? – is part of its power of course. Though I hadn't read The Female Eunuch, I'd heard lots about it – mainly icky rumours of exhortations for women to squat over mirrors and feast on their menstrual blood. As Germaine puts it: "If you think you are emancipated, then you might consider tasting your menstrual blood – if it makes you sick, you've got a long way to go, baby." Well, I may still have a long way to go, baby, but I'm now sure of one thing: The Female Eunuch has just as much to say to a 28-year old in 2010 as it did to my Seventies sisters.

Less than 250 pages long, it's a short, sharp shock of a book – even in my 2006 bumper edition with its girly, cerise-pink makeover. (What would Germaine make of that, I wonder? This happens a lot, by the way, when you're reading The Female Eunuch. You find yourself asking WWGD, or What Would Germaine Do?, at odd moments. The answer is usually: snort derisively.) She likes to begin and end the brusque chapters with a bang: "Women's sexual organs are shrouded in mystery", "Women have very little idea of how much men hate them" – that sort of thing. There's plenty to be shocked by (the "penis weapon" and "cunt hatred" make frequent appearances), and plenty to be depressed by. According to Germaine, our enemies are everywhere – "doctors, psychiatrists, social workers, marriage counsellors, priests, health visitors and popular moralists" – and the traditional route of marriage and children amounts to little more than a living death. "Mother is the dead heart of the family, spending father's earnings on consumer goods to enhance the environment in which he eats, sleeps and watches television."

There's also, though, plenty to be joyous about, not least its celebration of the female body and sex. After all, "the struggle which is not joyous is the wrong struggle". It's unexpectedly, very witty, too. Her deconstruction of a swooning Barbara Cartland love scene had me sniggering on the Tube. At university, I had grappled with feminist literary theory for a term, reading endless po-faced papers by French feminists with alarming titles such as "Castration or Decapitation" and "Speculum of the Other Woman". Here, though, was something so much more practical and humorous, so much more rousing and joyful, to help me negotiate my position as a woman in the world. Feminism could be funny!

Some of Greer's ideas are brilliant – her writing on the body and female stereotypes in media, art and literature is, I think, definitive – and, in our airbrushed, silicon-enhanced world, more urgent than ever. If you read only one chapter, make it "The Stereotype": "I'm sick of pretending eternal youth. I'm sick of belying my own intelligence, my own will, my own sex. I'm sick of peering at the world through false eyelashes, so that everything I see is mixed with a shadow of bought hairs..."

Some of her ideas are wrong-headed – her suggestion that women bring violence on themselves is particularly repellent, couched as it is in superior tones: "I have lived with men of known violence, two of whom had convictions for Grievous Bodily Harm, and in no case was I ever offered any physical aggression, because it was abundantly clear from my attitude that I was not impressed by it." I find it hard to sympathise fully either with her most pessimistic views on womankind and the stifling straitjacket of the family, or her rose-tinted utopian views of how an ideal society might function (a commune overrun with shared children and shared consumer goods in Calabria seems to be goal). But what a pleasure to be whipped along in her argument. Everything is looked at afresh, with a sniper's eye for detail. Even ballroom dancing gets it in the neck. ("An extraordinary capitulation on the part of society to the myth of female submissiveness: the women travel backwards, swept along in a chaste embrace", apparently)

It's a polemic, and a dazzlingly argued one at that. It's designed to raise objections whatever age you read it in. But is it relevant? This week, the Australian writer Louis Nowra stuck his oar in (Germaine would have plenty to say about that phrase, but that's by-the-by), saying that reading the book was "like opening a time capsule". To the 21st-century reader, some details feel like anachronisms. Her examples of working women are confined to typists, shop-girls and nurses; female students at university are put under the microscope as a strange species; and her hostility to the contraceptive pill and cervical smear tests comes across as hopelessly old-fashioned, if not downright dangerous. Society has moved away (though not entirely) from the model nuclear family she concentrates so much of her energy on attacking.

A product of its time, it's hard to imagine today just how shocking it must have seemed when it first landed. To contrast, my mother, one of the few girls at her school to go to university, showed me a copy of The Girl Book of Careers my grandparents gave her when she was growing up. Published just a decade before The Female Eunuch, it offered insights into life as a secretary, a window dresser, a florist, a shop assistant, an actress and a cook, among other ladylike professions. Greer's book built on a growing feeling that once women gained access to university education, it was time to aim higher. "It was ground-breaking to put that into print," my mother recalls. "Women of my set were all reading it. I'm quite sure an awful lot of women weren't reading it. I don't think we were particularly militant, but I felt it was very important to use the education I'd worked hard to get. I did not feel it was right for women to sit at home being second-class citizens." Greer gave that feeling a voice. When she stood up opposite Mailer in New York City Hall in 1971 and yelled, "We broke our hearts trying to keep our aprons clean!" she was greeted by rapturous whoops and stamping feet.

That parts of the book now feel like a "time capsule" is proof of its success, isn't it? In a foreword written to celebrate The Female Eunuch's 21st birthday, Greer herself admits that she thought "the book should quickly date, and disappear" on publication. The fact that it has done neither shows that we still need to read it, to see how far we've come – and how far we still have to go. Appearing on The Review Show this month, Greer was in no doubt that her original message was still pertinent, still needed hammering home. "You didn't get emancipation!" she said. "You didn't get it for goodness' sake! The feminist revolution hasn't started."

So the fight continues. And there does seem to be something in the air at the moment. Martin Amis has told anybody who will listen that his new novel, The Pregnant Widow, is about feminism. Set in the year The Female Eunuch was published, it details the cataclysmic effects of the sexual revolution on a group of young Seventies friends. "Every hard and demanding adaptation would be falling to the girls," he writes. "The boys could just go on being boys. It was the girls who had to choose." Natasha Walter's Living Dolls: The Return of Sexism sees her regret the sexual emancipation she once championed and lament the rise and rise of "raunch culture" and the "pinkification" of young girls. Kat Banyard of the Fawcett Society is about to publish The Equality Illusion. Elsewhere, the biggest hit of the Edinburgh Fringe was Trilogy, a joyful celebration of women and their bodies. The wonderful Mad Men is praised for its subtle evocation of the changing sexual mores of the Sixties, through the tales – more or less empowering – of ambitious Peggy and Betty the bored housewife. The prospect that Kathryn Bigelow might be about to be the first woman director (ever!) to win the coveted Oscar this weekend has the film world buzzing with feminist debate. And online, from web giants like Jezebel to blogs like XXrayspecs, women are subverting mass media images of airbrushed, oppressed womanhood from within, pointing them out, poking fun at them and getting millions of hits in the process.

All of which seems to point to the fact that, 40 years on, feminism is back. We've still got a long way to go, baby – starting with the word itself. Since The Female Eunuch was published the F-word has become first a dirty word, then an irrelevant word and finally a confused one. "I used to say that I avoided the word because of its negative connotations," says Lionel Shriver who has written an introduction to Betty Friedan's 1963 tract, The Feminine Mystique, republished this month.

"It seems to convey that, if nothing else, you have no sense of humour. But it's important to reclaim that word. An awful lot of young women really avoid the word and think they don't need it, that they don't need the movement and they don't need the politics."

The prevailing idea seems to be that feminism has gone too far: having demanded it all, got it all, women now can't cope with it all. An article in The Times last month declared that 40 years of feminism had "made women less happy". Amis and Walter share a certain wistfulness for the pre-sexual revolution days, while Amis has said that the feminism is still in its "second trimester", thanks to women buckling under the new restrictions of having to hold down both a job and the household. "Most families now can't afford to live without a second income. It made work seem less of a privilege – it's now a necessity", says Shriver. "There's a live movement that romanticises the 1950s model. The Feminine Mystique and The Female Eunuch are good correctives on that romanticism, because the truth is that when women were expected to do that, they got depressed and bored to death."

In other words, we still need these books to remind us never to go back. The Female Eunuch changed many things, but not everything. To borrow a phrase from the distinguished lady writer herself, "it's time to get angry again". And I need to go out and buy a T-shirt.

Germaine Greer: Life and times of a feminist

1939 Germaine Greer is born on 29 January in Melbourne, Australia. She is the first child of Margaret Mary "Peggy" and Eric Reginald "Reg" Greer.

1942 Greer's father joins the Australian Imperial Forces and leaves for war. It is two years before she sees him again, during which time she becomes the centre of her mother's attention. Her 1989 autobiography, 'Daddy, We Hardly Knew You', tells part of that story. And while one of her books characterises the love of mother and daughter as the most beautiful of all, she is later estranged from her mother.

1956 Wins a teaching scholarship after attending a private all-girls' convent school, Star of the Sea College. Graduates from Melbourne University with a degree in English and French. Moves to Sydney in 1960 and becomes involved with the left-wing sub-culture group Sydney Push and the anarchist Sydney Libertarians.

1964 Moves to the UK to study at Newnham College, Cambridge. By 1967 she has a doctorate, and is a member of Cambridge Footlights. Using the pen name Rose Blight, she writes a gardening column for 'Private Eye' and contributes to underground magazine 'Oz' under the name Dr G.

1968 She marries Paul de Feu; it lasts three weeks, during which Greer later admits she is unfaithful several times.

1970 Publication of 'The Female Eunuch' turns her into a household name. She poses nude for 'Oz' magazine and also the Amsterdam underground magazine 'Suck', of which she is editor.

1990 Greer makes the first of nine appearances on the panel game 'Have I Got News For You', setting the current record for a female guest.

1996 Resigns her role as special lecturer and fellow at women-only Newnham College after opposing the election to a fellowship of a transsexual colleague, Dr Rachel Padman, on the grounds that Padman was genetically male.

1999 'The Whole Woman', intended as the sequel to the 'Female Eunuch', is published. The following year she poses nude for the Australian photographer Polly Borland.

2000 Greer is assaulted in her home by a 19-year-old female student from Bath University. The infatuated student screams at Greer, calling her 'mummy', ties her up in the kitchen and smashes her belongings. Friends whom Greer was meant to have met for dinner that night later find the author lying distressed on the floor, with the student hanging onto her legs.

2003 Publishes an art book about male teenage beauty, claiming "society is not accustomed to seeing beauty in young males".

2005 Appears on 'Celebrity Big Brother' but walks out of the house after five days.

2006 Presents a Radio 4 documentary on the life of her friend, Frank Zappa. (She has said she wants Zappa's 'G-Spot Tornado' to be played at her funeral.)