She stole the show in Robert Redford's The Horse Whisperer; Sofia Coppola cast her without an audition and she happily stepped into Kate Hudson's shoes ... No wonder Scarlett Johansson is setting temperatures soaring, says Polly Vernon

It took some time to convince Scarlett Johansson that a lingering shot of her bottom, encased in sheer, pink pants, was categorically the only way that director Sofia Coppola could open Lost in Translation, officially the hottest film of next year. Johansson had reservations. 'I really didn't want to do the sheer underwear,' she says. She's not being coy about it. Coy isn't in her repertoire. It doesn't go with her voice, which is low, sardonic, fag-filled. 'I told Sofia. I said, I'll wear underwear, if it isn't sheer. I had to wear underwear, like, the whole movie. It became very easy for me to trounce around in my underwear, in front of a large group of Japanese men. A skill I probably won't utilise again, admittedly. But sheer... sheer was... different.'

Coppola talked Johansson round. She wanted sheer pink underwear. She'd written precisely those pants into the script. She knew which brand she wanted. Coppola's an aesthete. These kind of things aren't negotiable. And in the end, after Coppola had modelled the pants personally, and Johansson had admired the way they looked on her director's minuscule frame, she agreed.

'I was happy that it looked as nice as it did,' she says, finally. 'I told Lance [the director of photography], "If you make my arse look bad, you will never work in this town again!" He was, like, "I promise, it will look really nice." I was, like, "OK, I'm trusting you." And it did. My arse looked OK.'

Scarlett Johansson's good arse is just one of the things that allows her to tick every box on the rising hot-young-thing checklist, with an almost disinterested languor. She is beautiful in an evasive, interesting way. Her eyes are huge and blue and knowing, her eyebrows are winged, her lips are indecent, her expression is sharp and aware and absorbing.

And Scarlett Johansson is hip. Traditionally, 'actor and cool in an uncompromising fashion' are mutually exclusive notions. The unseemly scrabble for recognition, and the hard-edged ambition that accompanies the progression towards super-stardom, generally mean you have to sacrifice things like cool, in the name of rampant self-promotion. But Scarlett hasn't. On the contrary, she oozes fluid cool like other people ooze sexiness.

She's barely 19 years old, though you wouldn't know it to talk to her. Robert Redford, who worked with her on The Horse Whisperer, described her as 13, going on 30. She's a New Yorker, and New York years are worth double everyone else's, in terms of accelerated dry, wry urbanity. ('Although, actually, I don't know if that comes from being from New York, or from being... me,' she says.) She's got a great name. A film star's name. And, as we have already established, a great bottom.

But more than this, Johansson has enormous talent. Vast and uncompromised, it's the most significant of her generation; but also the subtlest. Until very, very recently, her talent was on slow burn. A succession of smallish roles in biggish films (which she often landed after a higher profile, less capable actress passed on the project), or major roles in offbeat independent flicks, have defined her career, and kept her semi-obscure. Edited highlights: she made her big-screen debut at 10 in Rob Reiner's North, played Robert Redford's young patient in The Horse Whisperer when she was 13; at 16, she won whatever the indie equivalent of wild acclaim is, for her sneering teenager in Terry Zwigoff's Ghost World.

But, following nine years of quiet accomplishment, 2004 will belong to Johansson, in a high- octane, unapologetic, Oscar- snaring sort of a way. It will be the year in which she graduates from exquisitely promising starlet on-the-verge, to fully blown movie establishment. And she knows it.

In the flesh, Scarlett Johansson is pretty much as intimidating, self-contained and impressive as a person can be. She is magnificently well-dressed, poised, powerful. She is polite, but you can sense a reservoir of terrifying scorn and dismissiveness sloshing about just below the surface, and you wonder when she'll draw on it. She is quite obviously the girl who, when asked how she felt about style magazine The Face's assertion that she does 'dour contemplative angst to perfection', sighed, and then said: 'Dour, contemplative angst? Well, those are all SAT words. Hold on, I'll get a dictionary.'

After dominating a press conference (outshining both Sofia Coppola and producer Ross Katz simply by being unexpectedly peroxide blonde and a little bit sullen), she coils her small, cool self up in a chair of substantial chintz, in her suite at the Dorchester, and accepts my congratulations on her excellent choice of footwear. 'Well,' she says, slowly, deliberately, with measure. 'Aren't I a trendster?'

Two roles in two spectacular films will send Johansson stella in 2004.

In Coppola's rapturously received Lost in Translation, she plays Charlotte, a lonely, jetlagged 22-year-old, killing time in a vast, luxe Tokyo hotel whilst her increasingly distant photographer husband (played by Giovanni Ribisi) works. She meets Bill Murray's middle-aged, hapless and unhappy Bob Harris, a fading movie star reduced to filming a whisky commercial in the city; they save each other. Their unconsummated, understated love affair is one of the most compelling, gentle things ever to make it to multiplexes, and as staggering as Murray's performance is, Johansson is equal to it. They are both heavily tipped for Academy Award nominations.

In Peter Webber's adaptation of Tracey Chevalier's book Girl with a Pearl Earring, Johansson plays Griet, fictionalised almost-love interest of Colin Firth's Dutch artist Vermeer. Johansson was cast after Kate Hudson ducked out on the role, and the moody, delicate film, you suspect, is a great deal better for it. Both Charlotte and Griet could have been custom-created to showcase Johansson's particular talent. They are intensely reserved, quiet roles, although they aren't shy-girl roles. Scarlett's very grown-up capacity to communicate an incredible amount without lines or overblown emotional outburst, is her shtick.

'She makes you feel like she has been around the world,' Coppola, who hired Johansson after one, brief lunch meeting in a Manhattan diner, says. 'She has a coolness and a subtlety that you would not expect. You feel like she's seen a lot. She can convey an emotion without saying very much at all.'

Today, the emotion Johansson's conveying without saying very much, is predominantly under-whelmed ennui. She was pleased that Coppola was so impressed by her, of course. But, you suspect, not entirely surprised.

'It was... flattering,' she says. 'I heard she had a hankering after meeting me. That was good. And it meant I did not have to audition. Luckily. So there was no exhausting wait, or, a time when I didn't know what was happening. I just kind of always knew it was going to be... me.'

The film happened quickly. They shot for 27 days in Tokyo, and stayed in the Tokyo Hyatt, in which most of the on-screen action took place. Johansson's overpowering impression of the shoot was of being 'busy, vulnerable and tired'. Bill Murray, she said, was either 'on', doing his comedy-Bill thing, or he was 'off', unreachable. No, spending time with Sofia Coppola was not like hanging out with the coolest girl in school. 'Yeah, she's quite cool, but... "coolest kid in school"... that has bad connotations for me. She is more like the quiet girl in the corner.'

Scarlett Johansson is clearly not over-awed by the promise of incredible success. She expects it. She has always been a fiercely ambitious individual. She admits to that freely. 'I have always... expected a lot from myself.' For as long as she can remember, she was, she says, 'a big ham, it's like I hopped out of the womb and said: I will perform!' At seven, she threw a tantrum during a tentative reccie round the offices of a talent agency, because the agency didn't want her. 'The only person they wanted was my older brother who couldn't care less, and who never ended up doing anything,' she says. There was a lot of potential for sibling rivalry - not only with Adrian, her elder brother, but also with her sister Vanessa, her twin Hunter and an older half-brother who lives in Denmark. 'I was, like, devastated. I decided at that very moment that my whole life was going down the tubes. And my mom was, like: I didn't know you were that interested. And I was, like: yes, yes! How could you not recognise this in me?'

Convinced she had found her metier, Scarlett (by now eight years old) ditched ballet classes and launched herself on to the advertising audition circuit: 'That thing where you turn up and they don't know if they want someone who looks like you, or a six-year-old Chinese boy.' She hated it.

'It was like being in a beauty pageant. The other moms were really scary, and it was awful, a really sordid scene. So I'd throw tantrums and my mom [who was her manager until recently] was, like: I don't want to do this any more! And then I was, like: you can't take this away from me! She was, like: fine, but I'm not going out on these commercials. So I just went out for film. And I never had another complaint. I felt like they weren't casting me because I had long blonde hair, they were casting me because I had something to offer.' She was no Macaulay Culkin. Her voice was too low, her appeal, even then, was too edgy for cutsie kid-flick success. Not that Johansson would have embraced the mainstream-pleasing Home Alone variety of mega-vehicle, had it been offered her. It isn't her style.

'After I did The Horse Whisperer, I got a whole slew of scripts about girls who were getting raped and cut into little pieces; or, you know, girls who were horseback-riding champions who then got some fatal disease, all these Cinderella stories, or heart-breaking stories, or disgusting slayer stories. And because I wasn't supporting anybody, like I wasn't supporting my family, I was just able to do whatever I wanted to do, films like Ghost World, and not worry about how much the box office was making.' If agents pressurised her to take on big projects, she fired them. 'I was, like: "Obviously, you don't understand me, or what I'm about, so why are we working together?"'

These days, apparently, Johansson's mostly getting a a pile of scripts that cast her opposite older love interests. Firth in Girl with a Pearl Earring, Murray in Lost in Translation. And though it's a tribute to both Murray and Johansson that, despite the 34-year age gap, Charlotte and Bob's relationship doesn't make you want to cringe and despair of a culture that cheerfully endorses the notion that young, beautiful girls will always fall in love with men old enough to be their fathers; nonetheless, you have to wonder if Johansson's in danger of being typecast. 'Is that a typecast?' she asks. 'The ingenue? I don't think so.' In danger, then, of becoming a sex object for middle-aged men. 'I think young girls are always in danger of becoming sex objects for middle-aged men. And that's the truth of it.' Given the choice, she would, she says, rather be a sex object for younger men ('Wouldn't we all?') but, generally, she's enjoying this new variety of attention, wherever it comes from. 'I think a lot of that has to do with the fact that I finally became an adult,' she says. 'People wouldn't say: sexy 15-year-old Scarlett Johansson... that's gross. But now...'

('Well, she's legal now,' observes Sofia Coppola, archly. 'Yeah. Thanks, Sofia,' says Scarlett.)

'Now, it's great to be able to pronounce your sexuality. Not... over-annunciate it. But use it, touch on it. I'm a very sexual person, I have a sexual energy about me that I'm very proud of. Like my femininity, and I think it's nice, to have guys and girls think you're sexy. As long as it's not tacky.'

Occasionally, Johansson lets her phenomenal composure, her borderline spikiness, her veneer of Manhattan hip kid, slip a little, and gives you a glimpse of something sweeter and more accessible beneath. She says that one of the best things her nascent celebrity has offered up was the opportunity to meet Patrick Swayze, most unlikely among cool-girl pin-ups. 'Yeah I did. Woo hoo! Although I would have tracked him down sooner or later. No, but that was joyous.' And random public animosity disturbs her. 'I've read certain things... it gets... disappointing. I went online and found this thing: "Oh God, she's so ugly, and she's so not talented, I don't understand what the big deal is..." I was, like: "Why are you being so mean? I'd like to know what you look like. And who has the time to go online and talk about people they've never met? And be so very serious about their chatroom conversations? My God, what else do you have, a postage-stamp collection?"'

But her life is good. She is single ('For, like, the first time since puberty basically') and she feels glamorous. 'Oh, always, even when I'm not very glamorous at all. If you feel glamorous, you definitely look glamorous. Though right now, I'm not feeling very glamorous at all. I feel like quite a frog, actually.' She isn't terribly rich ('Oh, all the riches I have earnt from all these independent movies!') but she's richer than she would be if she'd never stepped foot on a movie set. Rich enough to buy 'some art', and an apartment in LA, at least. She splits her time between it and the home of her Danish building contractor father in New York. Her I'm bi-coastal. Yes, I am. That's glamorous.'

She doesn't think she has an enormous capacity to go off the rails, even as her celebrity is cranked up a few notches, and the opportunities for rampant debauchery present themselves more frequently. Her greatest vice, she says, is cheese. 'Nothing else reigns over my life. I don't have a cocaine problem or anything. Waiting for the cocaine habit to kick in, actually.' But it's tough to imagine how her work schedule and her steely self-control would accommodate that sort of thing.

Johansson is spoilt. She can be difficult. If a question doesn't impress her, she lets you know. When I ask her what it is that Bill Murray whispers to her in the final scene of the film, the secret thing, the thing that makes her character Charlotte smile like everything will be OK in the end, she says: 'Oh, you think you're the first one to ask?'

She won't sit on the floor for pictures. She trails entourage. Her publicist is fiercly restrictive regarding access to her charge, banning me from the photoshoot, thus adding to her mythology. But that doesn't mean that Scarlett isn't rather intriguing in the flesh, and mind-blowing on the screen.

Ultimately, you suspect that anything but acting bores her, at least a bit. Ask her about her forthcoming filming schedule, and she becomes virtually effusive. 'Yeah, I'm excited. Really excited. I can't believe I'm going to be around all that equipment in a week,' she says. 'I'm going to have people put my marks down... and I'll be eating catering with the rest of the crew... It's nice. It's great to work. It makes me feel useful.' She pauses. 'It makes me feel like somebody needs me.'

· Lost in Translation is released on 9 January and Girl with a Pearl Earring is out on 16 January.