One evening in October of last year, after a reported couple of drinks in a Brooklyn bar, Rupert Murdoch was giving a good impression of a man who thought he had seen the future. From his car on the way home he tweeted: "Who's heard of VICE media? Wild, interesting effort to interest millennials who don't read or watch established media. Global success."

The months since have served to emphasise the Digger's clairvoyance. If you hadn't heard of Vice media back then, it is likely that now you have. In America, in particular, two archly millennial Vice stories have made the "established media", Murdoch included, look distinctly 20th-century by comparison. The first involved the on-the-run internet millionaire, John McAfee, whose paranoid tale of drugs, murder and subterfuge in the jungly paradise of Belize dominated the daily news channels and blog sites for a few weeks before Christmas. When McAfee surfaced, having gone into hiding after being sought for questioning over the death of his neighbour, it was in the company of not only his 18-year-old girlfriend, but also a couple of young reporters from Vice. While the rest of the world's media, as well as the Belize police force, had tried to track McAfee down, Vice had helped to smuggle the fugitive over the border into Guatemala, and also, in true chaotic gonzo fashion, succeeded in inadvertently revealing his whereabouts in a blogged photo, which carried the message, "We are with John McAfee right now, suckers!"

The second Vice scoop was perhaps even more incendiary. Last month a documentary film crew from Vice blagged its way into North Korea in the company of the NBA legend, and celebrity rehab casualty, Dennis Rodman, and the Harlem Globetrotters. The Vice crew once again could hardly believe its fortune when Rodman ended up befriending Kim Jong-Un, the recently installed supreme leader of the world's most repressive regime, and now, apparently a basketball fan. Over the course of a couple of days, outtakes from this unlikely bromance were sent from the Hermit Kingdom via Vice.com and provoked predictably manic viral attention.

When I visit Vice's offices in Brooklyn, co-founder Shane Smith has spent the weekend both defending Rodman's "basketball diplomacy" and revelling in the media storm that has attended it. The story, a trademark mix of laddish farce and harder-edged foreign affairs is, he suggests, pretty much the perfect Vice exclusive. "The thing is: Dennis Rodman is absurd. North Korea is absurd. And our whole mission statement at Vice is the absurdity of the modern condition. So it made perfect sense for us." Smith is amused and frustrated in about equal measure by the generally outraged response of Fox and CNN and the New York Times and the rest. Above all it demonstrated, he says, a certain kind of unease – perhaps even envy – at the Vice philosophy of what he calls "immersive" journalism.

How much, I wonder, did Rodman, the lavishly pierced and tattoed former lover of Madonna, know about the trip in advance?

"Well I think he was keen to go play a game with the kids there but I don't suppose he quite got the gravity of what he was doing and where he was going. He's not a diplomat. And frankly we did not know that Kim Jong-Un would show up. When he did, we thought: 'Oh, OK, what happens now?' And then, when he said, 'Hey, everyone come back to my place for dinner!' we were quite gobsmacked."

In some ways it was a logical conclusion to what has been a long-term obsession for Smith. He visited the police state a couple of times in 2007 to film The Vice Guide to North Korea, a documentary of pre-conceived weirdness which did not stray far from what heavy-handed minders allowed. Smith was, in any case, subsequently banned from returning, but felt he had unfinished business in Pyongyang. He believes the Rodman stunt served a wider purpose, giving his film crew "unparalleled access" to the regime for a documentary on which they are still working.

"People turned round and said we ate food with this guy [Kim Jong-Un] and people are starving in North Korea. So you are saying no diplomat can ever eat food with a bad leader? That's half the world gone. It's just we had an idea of how to get in and how to get access and it worked. But when people like [former Clinton spokesman, now a TV political journalist] George Stephanopoulos ask Dennis Rodman about foreign policy and people are surprised he doesn't understand all the subtlety, I mean who is shocked by that?"

Is it journalism in any sense, though, or just a curious, contrived spectacle? "Well," he says, "we are getting a story that everyone is interested in seeing and nobody else could get. People call us 'adventure journalists' or 'daredevil journalists' or whatever. But in an insane world the mad way often works …"

Smith has high hopes that the Rodman documentary will surpass the million-plus hits reached by Vice's 2009 interview, by Smith himself, with Joshua Blahyi, known as General Butt Naked, the cannibal warlord of Liberia. "Both are crazy stories with sad and tragic underpinnings," he says. "But a news story for us is the same as for everyone; we like our stories to punch you in the face."

Does he ever feel that he weights his stories more to the punch in the face, and less to the sad and tragic underpinnings?

"The easy answer is no. If you look at the story we did about the slave labour camps of Liberia," he says, [another strand of the Vice Guide to Liberia] "we broke the story, it was an important story. This guy General Butt Naked killed 20,000 people and ate some of them. I don't know how you would go about further sensationalising those facts."

Shane Smith is a burly 42-year-old Canadian, whose vast glass-sided office is dominated at one end by a stuffed grizzly bear in front of a blown-up photo of the snow-capped Rockies. He is a direct and charming talker, but he carries just the vaguest hint that if there were any literal punching in the face to be done, he would not be taking a step back. The Vice offices are in a corner of recently gentrified Williamsburg, on a street decorated with expensively commissioned graffiti and bookended by slightly contrived boho cafes. The office itself is on the site of a former brewery, but any sense that this is a sort of slacker's paradise is dispelled when you step inside, and teams of intense twentysomethings are busily convening everywhere you look to discuss this magazine spread, or that mobile platform, or the latest YouTube offering or marketing collaboration.

Vice has come an awful long way from its origins as a free and underground music magazine in Smith's native Montreal 20 years ago. He created it with a couple of friends – having persuaded the city fathers to let them take over an earnest community title called the Voice. In the two decades since Vice dropped its middle "o" it has grown from being a "hipsters' bible", given away on street corners and in record stores, to a global brand with offices in 34 countries. The high-traffic online and documentary film incarnations of the Vice sensibility are about to spawn a 24-hour terrestrial news channel available in 18 countries. A documentary series in partnership with august HBO will include the Rodman and McAfee films. There is also a record label and an ad agency, Virtue, which numbers Nike and Dell among its clients. Announcing some of those departures at an industry event in Abu Dhabi last year, Smith envisioned "a changing of the guard within the media," and announced his ambition for Vice to become both the largest online media network in the world and "the voice of the angry youth".

To back up this fighting talk, Spike Jonze, the disruptive intelligence behind the film Being John Malkovich and the Jackass franchise, was installed in 2007 as creative director. Two years ago a consortium that included Sir Martin Sorrell's WPP advertising group, and Tom Freston, founder of MTV, invested a reported $50m in Vice media. Since the company purchased Vice.com (formerly a porn site) the same year, revenues have doubled to a reported $200m in 2012, on which insiders suggest an unverified 20 per cent profit margin. Smith talks of 3,000 contributors, though the official payroll is about 850. The average age of a Vice journalist is 25, but scanning the screen-staring ranks of the magazine's newsroom that seems on the high side. It is easy to see why, on his visit here, Rupert Murdoch might suddenly have felt all of his 82 years.

Smith retains a centralised control of his ever-shoutier multi-platform mouthpiece. "We have a global editor, then we have domestic editors and content directors each country that we are in," he says. "They send in the stories they want to do and we say 'great, let's do it', or 'no, let's not do it'. And we make a call that this would be good for online, this would be good for mobile, this would be good for the mag, this would be good for TV and so on."

He remains insistently involved with every stage of that decision-making. "We are releasing so much content now," he says, "that there is a probability otherwise that it will run away with itself. You know, if you are Henry Ford you better give a shit about making cars. And if you are making grapple grommets you better give a shit about grapple grommets. We are in the business of creating content so I better give a shit about that."

Before meeting Smith I've been trying to get a proper immersive sense of what that content might include. There is above all a sort of attention-deficit quality to Vice's output, shifting abruptly between tones and sensibilities. To take just the current magazine for example, lengthy closely reported articles about expat Jewish Americans settling illegally on the West Bank and the rise of Swedish fascism rub up against vaguely cruel spreads about Elvis lookalikes and high-concept fashion shoots. There is a voyeuristic Dazed and Confused edge to a lot of it, done with the production values of National Geographic, and occasionally the kind of easy misogyny that has seen the magazine banned from campuses (though Smith insists that the readership, particularly online, "is not skewed as much to the male as you might think – no more than 60 per cent"). Regular features include "Do's and Don'ts" which offers a surrealist commentary on random snapshots of people, fashion victims and other candidly photographed unfortunates, in the street or in clubs or bars, sometimes bleakly funny, sometimes laced with the kind of bullying rhetoric of anonymous blogging. Alongside that there is an indefatigable effort to find a musement in the world – there have been popular "Vice Guides" to everything from anal sex to Mecca – and a commitment to understanding, however brutally, or surreally, the margins of global culture. The writing owes something to the golden age of British style and music magazines, the Face and NME and the rest, self-consciously erudite or smugly postmodern, and something to the packaged curiosity, and patient storytelling, of Reader's Digest.

Smith and his less visible co-founder Suroosh Alvi have the unusual ability both to curate this slightly dysfunctional mix and sell it smoothly to advertisers and anyone else who might listen. He gestures intermittently toward his and the magazine's "DIY punk origins", but you guess he was always more Malcolm McLaren than Johnny Rotten. "We were a quintessential Gen X magazine, and we are now a quintessential Gen Y company," he will say.

How does he define that particular alphabetical shift? I wonder.

"Well," he says, "20 years ago we were the hipsters' bible and all that crap, and then we went online, and famously, or famously at least in Vice lore, we reinvented ourselves. We like to say, in reference to Dylan, 'We are not afraid to go electric'. We let our very high-profile editors go. We handed the thing over to kids straight out of school and let them run our magazine. And that has allowed us to become this Gen Y platform. It took us 10 years to get to a million copies of the magazine, and it took us one year to get to 10m uniques [online browsers] a month."

And how does he measure success himself?

"For me personally, you always think when you are starting out, I am going to make a nebulous amount of money, buy an island, wear an Amadeus wig and go naked and be crazy. But, you know, I was talking recently to Spike [Jonze] and he said 'Take money out of the equation. And ask yourself what would you do?' and I realised two things: first I would pay money to do the job I am doing, and second I wanted to build the next CNN, the next ESPN. And I also realised that given the digital revolution that is not only within my grasp, but I am frontrunner to get there. Once I realised money isn't the report card, and putting your imprint on the world's cultural fabric is possible, that is when we stopped scrabbling around on the periphery begging for money, and thought 'let's go for it'."

It may not sound much of a business plan, but the money duly followed "in buckets". It's in Smith's interest to say so, but you pretty much believe him when he suggests that every private equity firm or media corporation around has tried to buy Vice at one time or another. Rupert Murdoch was only the latest mogul enthusiast for the company, he suggests.

"We have had everyone in here. Hearst, Time, Condé, Google. It was funny, we were in a meeting with News Corp and Rupert walked in, and I said, 'You should come by the office some time, check out the shop'. And he said, 'Well let's go now'. So we drove out here and I walked him round, we had a drink in a bar round the corner. And I suppose because he is recognisable people started tweeting…"

Smith explains Murdoch's fascination with Vice as only natural. He has the feeling that in the "boardrooms of every major media company they are saying, 'OK we need Gen Y, we need online, we need social, we need mobile, and we don't have any of that stuff. We need it globally, we need scale and we need to be able to monetise all that.' So they look around to see who ticks those boxes and eventually they come to us. They come out here and see all the kids working 18 hours a day and everyone really passionate. They think, 'Yes, we have cracked the internet code!' And they are so used to everyone saying yes, to people who have been waiting for their Amadeus wig all these years, that when we say actually we are not really interested in selling, they keep offering us more millions."

Smith developed some of his business acumen in his gap year after studying political science at Carleton University in Ottawa, when he apparently set himself up as a black-market currency trader in Budapest at the time of the fall of Soviet communism. For a while he says, he was earning more in a day than doctors there earned in a week. That kind of thing. Having been "a real leftist, working for Greenpeace and all that" he consequently developed something of a taste for edgy capitalism. Even so, when he returned to Montreal and started the magazine, he couldn't understand how anyone could buy a car, or why you would want a mortgage. "But once you have a family and kids you realise the importance of those things."

Smith has two daughters, now, aged three and one. I wonder, eyeing the grizzly bear at his shoulder, if fatherhood has put him more in touch with his feminine side?

"It is funny," he says, "I was in Libya with a bunch of mujahideen jihadists doing a story when I heard that my second baby would also be a girl, and when I told them they were all so thrilled, 'Allah has blessed you!' And I said I thought it was kind of interesting in such a male-dominated culture for them to be so excited that it was to be a daughter. They said "No! A man needs daughters, they will love you forever and never leave you, unlike sons who are off at the first opportunity."

Smith himself is a case in point in that regard. Though he talks about a very happy childhood, he also claims to have left home and got himself a job and a place to live aged 13 – "I was in a bit of a gang, a headstrong guy". Not for the first time, in talking to him, I have the sudden sense that his father, a pioneer computer programmer amongst other things, might have been something of a tough taskmaster.

He laughs when I suggest that. "He was. My dad has always been like me but on steroids, a lot smarter than I am, a lot tougher than I am, sort of a George Bernard Shaw: taught himself everything. But the thing was he was never happy. It's my luck that I am that much stupider than him. When I graduated, I had a paper published in this political journal and everyone was so proud, and I remember coming home and he just destroyed my thesis. He knew more about it than I did even though I had been studying the subject for years. And he wasn't trying to knock me down, he just knew a lot about everything, theoretical physics, whatever, but he could never get it across. I my case I kind of lobotomised myself with booze and drugs early on but the one thing I had, I could sell ideas."

Still, Smith suggests, he can hear his father's voice in his head, when things have been tough, when the magazine was failing to begin with, or when he has tried to launch in new cities. "When I was a kid my dad told me two things," he says. "Life isn't fair and you have to be both the strongest guy and the smartest guy. He thought it was important that I could build a house from scratch, so I worked alongside him as he built one. From when I was eight years old we would go and get a car from the junkyard and work out how to get it running. That was the weekend."

Given he was forced to grow up early, it's understandable perhaps that the dominant sensibility of Smith's creation should have been a kind of permanent adolescence. He recently had the idea for a TV series about the generally parlous state of the world, and the mostly juvenile political response to fixing it, entitled "Where are all the adults?" Then he realised that perhaps he had the opportunity to be a grown-up himself. With this in mind he seems to visualise a future in which Vice comes of age with him, and becomes the voice of a more politicised generation, the one just now realising that it has been shut out from the opportunities enjoyed by those who have gone before.

"In the beginning," he suggests, in biblical fashion, of the first web generation, "there was this era online of let's just be cool and criticise everything, and we were very guilty of that. But as Josey Wales says, 'There comes a point when it is time to get busy living or it is time to get busy dying.' So we have been trying to say, OK we are going to go out and actually do stuff, get involved. We don't mind if people hate us, we would prefer them to love us, but we don't want indifference."

What kind of stuff will they do, though, beyond Rodman-style stunts? It is Smith's and therefore Vice's contention that we are approaching a kind of reckoning. The stories he is drawn to tend to have a red-in-tooth-and-claw apocalyptic component, whether he is documenting a two-week traffic jam in Mongolia, or featuring, as the current online offering does, the sewage flooded graveyards of Gaza, or describing what happens when you wear semen-scented perfume for a week. If you read only Vice, I'm pretty sure paranoia, possibly agoraphobia, would set in quite quickly.

This brand of stylised bleakness is evidence, he suggests, that "the cheque has now arrived – economically, geopolitically, environmentally – and the coming generation, Gen Y, are realising they are going to have to pay it. Would I like Vice to be a major part of the media that reflects that? Absolutely. If you look not just at the Arab spring, but at what I call the youth spring that has started in Europe, young people are starting to find a voice, and they are not looking to the traditional media to reflect that. CNN was made by the Gulf war. I think the economic crisis will prove to be our Gulf war. It is making young people very angry and we want to be the voice of that anger."

His commitment to the absurdity of the modern condition is one part of that rage, he says. "A lot of what happens in the world is full-on crazy and doesn't get reported on. We want to change that." He doesn't believe that the outsider generation Vice is speaking to will adopt old-style party-based politics any time soon, but will assume instead a far more eclectic and scattershot range of anger and passion. "Going forward it's clear that advocacy will be a hugely powerful force. If you dislike what General Motors is doing, you can overnight create a movement to tell people to buy Ford. What we want to do is provide more and more information to this generation to help them to bring that kind of advocacy."

Smith is clearly a man who warms to themes. Having started him on this line of thinking, he quickly gets into his stride, lecturing me now on the complacency of the western world, now on Vice's crucial role as agit-proppers-in-chief.

"In the early days it was kicking against the pricks," he says, at one point. "If we had received the press that we have gotten over this North Korea thing in the early days we would have all been walking up Broadway with our middle fingers in the air. We are not afraid to fight our corner, but we have a documentary team there still, we have a job to do. If that is growing up, then yes, we are growing up."

Smith routinely reserves the full blast of his frustration for the media status quo, the commentators and the columnists who don't set foot out of the door of their office and blithely assume that the world is pretty much as it always was. He can quickly rouse himself to the full rhetorical anger of the midnight blogger, while all the time carefully positioning his business as both the authentic voice of the outsider, and the new mainstream.

"American media has just become talk radio, incredibly partisan name-calling and op-eds," he says. "I think the wars in Iraq and Afghanistan proved it has completely failed to act as an effective fourth estate. And young people didn't sleep through that, as is widely believed, they learned instead not to trust what they were being told. Huffington Post and Drudge Report and all these things came up, exactly because people no longer had any faith in the traditional media. I am not saying either of those things are great, but they are a symptom of that loss of trust. I am not even saying Vice is great. I always say: if Vice has become a primary news source, then the world is completely fucked! I mean, we are still talking half the time about rare denim and sneakers!

"But the fact is four corporations own all of American news, and they are all equally scared of losing Budweiser or whoever as their advertisers. The greatest propaganda coup of the American right has been to convince its citizens that we are in the grip of a liberal conspiracy. As a result, Obama is to the right of Richard Nixon on most issues. And there is we believe, certainly some space to exploit there." He pauses, smiles, concludes his lesson for the day. "And we, Vice, aim to exploit it."

This article was amended on 25/03/13 to clarify the starting point of Spike Jonze's involvement with Vice.