Spike Jonze is crouched in the shade of a tree on the kerbside outside a restaurant in Guanabacoa, a dusty Havana barrio. Sitting a few yards away from his camera, on the verge, is Yoandys “Baby Lores” González, the biggest star of Cuba’s booming reggaeton scene. Lores, in a tight T-shirt and sunglasses, his black hair styled into points, is telling Jonze how he built a career in a country where state control prevents him from selling his music.

“I have to be the roadie, band manager, everything. I have to do it all by myself,” says Lores, speaking through Julio Pabón, producer, Vice on HBO, who is translating. Lores makes money when he performs concerts and shows, he says, and distributes his music — a fusion of reggae and more upbeat Latin rhythms — without the help of a record label (the state frowns on reggaeton and Cuban radio stations refuse to play it). This is frustrating, he says. Jonze asks him if he expects the recent thawing of Cuba’s relations with the US to accelerate political change. Lores nods. “I believe in the revolution,” he says. “But to be a true revolutionary, as Fidel [Castro] was, is to change what needs to be changed.”

Jonze is one of Hollywood’s most original voices. He cut his teeth making music videos for acts like the Beastie Boys and then moved into features, directing the critically acclaimed Being John Malkovich and Where the Wild Things Are. His most recent effort, Her, starring Joaquin Phoenix and Scarlett Johansson, was nominated for best picture at last year’s Academy Awards, while Jonze picked up the Oscar for best original screenplay.

Jonze, 45, does not have the jaded outlook of someone who has spent the past 15 years in Hollywood. Wide-eyed, curious and lacking cynicism, he has a sharp sense of humour. He is not in Cuba to make a movie. He is interviewing Lores for Vice, a brand which started out in 1994 as a music and fashion magazine and has evolved into a sprawling, youth-focused media empire spanning TV, digital channels and publishing. He is in Havana with his friend Shane Smith, Vice’s co-founder and chief executive, and a crew to film a segment for the company’s news magazine programme, which airs on HBO in the US. Vice also has a four-year deal to produce a daily, half-hour news programme for HBO and operates Vice News, an online digital channel, plus a network of other online channels (or “verticals”) specialising in subjects such as music, technology and sport.

Vice’s ability to connect with young audiences has won it many admirers among more traditional media companies, which are finding young, “millennial” viewers and consumers increasingly elusive. Rupert Murdoch was an early fan: in 2012, after meeting Smith for drinks at Vice’s headquarters in Williamsburg, Brooklyn, he took to Twitter to declare the company a “wild, interesting effort to interest millennials who don’t read or watch established media”.

The Cuba segment seems ideally suited for Vice’s HBO show, which focuses on edgy, colourful stories from world hotspots. Its reports have ranged from an investigation into the radiation caused by nuclear testing in Kazakhstan to a piece on Afghanistan’s child suicide bombers. Vice has been increasing its news coverage, winning plaudits along the way: the HBO series won an Emmy last year and it recently won two Peabody awards for video reporting on its online Vice News channel. In one of the winning pieces, a Vice reporter was embedded with Isis fighters in Syria, capturing the group’s terror-driven zeal up close for the first time.

The catalyst for Vice’s interest in Cuba came at the end of last year, when Barack Obama announced that the US would begin normalising relations, ending more than half a century of hostility to its island neighbour. I first heard about Vice’s plans for a Cuba report in February, when I saw Smith at a party. He had been to the country to scout locations, he told me, and would be returning to film. Keen to see Vice’s journalism and chief executive in action, I suggested that I tag along.

And so, two months later, I take an early-morning flight from New York to Miami with Jonze and Alex Detrick, Vice’s communications chief. In Miami we board a commercial charter flight and, 45 minutes later, touch down in Cuba.

Vice’s HBO show and digital channels need a steady flow of ideas and footage that can be edited into long-form television programming or shorter pieces that work better online. The Havana trip is to gather material for the HBO programme and Alex Chitty, the show’s perennially stressed producer, and his team have arranged several different shoots to capture how the thaw in relations with the US is playing out in Havana’s culture, politics and society.

Driving into central Havana from the airport is to go back in time 50 years. The US embargo on trade meant no American cars made it to Cuban shores and there are few vehicles on the city’s wide boulevards apart from a spattering of older US models — classic Chevrolets and Pontiacs from before the embargo that have been repurposed and retuned over the years.

Vice CEO Shane Smith (left) with Vice’s photography director Jake Burghart (with camera) and director Spike Jonze (second from right) outside the Museum of the Revolution, Havana

It is too soon to see signs of any economic upturn linked to the normalisation of relations with the US. The grand Spanish colonial homes and buildings seized by Castro’s forces in the aftermath of the revolution are crumbling after years of neglect but the people on the street seem happy to see us. A young boy asks Detrick where he is from: when he replies “New York”, the boy sticks his thumbs up and says, “America! Friends now!”

Our first stop is a privately owned restaurant in a Spanish colonial house in the city’s centre. The walls of the tall-ceilinged rooms are covered with antique clocks and framed pictures of newspaper clippings from the days after the 1959 revolution. With Smith are two camera operators, a sound man, a translator and a couple of local “fixers”.

The 45-year-old Canadian is wearing shorts which reveal a big tattoo on his calf, flip-flops and a black T-shirt. His bearded face is bright red, having caught the sun while shooting a segment at Havana’s Mariel port the day before, when he ran into a group of business executives from Florida looking for possible investment opportunities. Many people are piling into Cuba looking for the commercial possibilities that will open up as relations improve — we also encountered US baseball coaches scouting for local talent.

Jake Burghart, Vice’s director of photography, is arranging his camera to shoot Smith and Carlos Cristobal Marquez, the restaurant’s owner and head chef. Jonze, who is standing nearby, suggests that they change the angle of the shot; Smith, meanwhile, asks Marquez about running a private restaurant in Cuba.

“Restaurants used to be illegal here but now they are allowed,” Marquez says, explaining that the new generation of dining spots evolved from paladares — private homes which, in the early 1990s, were allowed to start serving small groups of guests. Smith wants to know how restaurants get their meat and vegetables in a country where all land is owned by the state. Marquez says restrictions on crop growth have fallen away. “The idea that you can even have a business now in Cuba is so new . . . it’s a big deal,” one of the restaurant doormen says to me, whispering so as not to disturb the shoot.

“The economy is getting better,” Marquez says. “Cubans who own businesses here have thrived.” His restaurant, which attracts a mix of tourists and locals, has a 1930s US-made General Electric cooker and, after filming a short piece in the kitchen, Smith tells me he is fascinated by the evolution of dining culture in Havana. “It used to be an underground economy,” he says. “Now it’s everywhere.”

He could say the same about Vice. When it started 20 years ago, it was a music magazine read by a few thousand hipsters and fashionistas; these days, its readership is close to a million. About a decade ago, Smith and his colleagues, at Jonze’s urging, began to focus on online video at a time when, thanks to YouTube, the medium was exploding.

The videos shot by Smith and his colleagues, and then uploaded online, introduced Vice to a much larger audience. In 2008, Smith and a colleague secretly shot The Vice Guide to North Korea, smuggling a camera into the country and filming everything they saw.

I’m only good at two things — making content and doing deals. Day-to-day business management is hard

Since then, the increase in the company’s valuation has been meteoric, with older, more traditional companies falling over themselves to invest. WPP, the marketing group run by Sir Martin Sorrell, bought 10 per cent of the company for $35m in 2011, valuing Vice at $350m. Two years ago, Rupert Murdoch’s 21st Century Fox bought a 5 per cent stake in a deal that valued Vice at $1.4bn; then last year, A&E — the cable television group owned by Walt Disney and Hearst — paid $250m for a 10 per cent stake, valuing Vice at $2.5bn. As part of the A&E deal, Vice will soon get its own cable channel in the US.

Vice will make more than $900m in revenues in 2015, up from $500m last year, Smith tells me. Based on this sharp growth, Vice says its values have risen to more than $4bn.

The deals have made Smith, the largest shareholder in Vice, very rich. At the beginning of the year, at the Consumer Electronics Show in Las Vegas, he won $1m playing blackjack at the Bellagio casino and spent $300,000 of his winnings on a meal for more than 30 employees and business partners. The bill was so eye-popping it merited a mention on the earnings call of MGM Resorts, the group which owns the Bellagio.

Podcast US rapprochement unleashes hopes in Cuba The US move to normalise relations with Cuba unleashed a sense of hope on the island, but the pace of change remains slow, as John Paul Rathbone tells Matthew Garrahan.

The restaurant filming complete, the crew begins preparing for the next shoot — an interview with a man who circumvents Cuban media restrictions by downloading and distributing US television programmes. But before that they want to eat, so we head to another restaurant in Old Havana. I get a lift with Jonze in a huge, lime-green 1955 Pontiac Vice has hired for the day and while we motor along the Malecón, the long roadway that hugs the coast, I ask him how he came to be involved with Vice.

“I loved the magazine,” he says, the sun glinting off the ocean behind him. He first discovered it in Los Angeles in the late 1990s, when he was editing Being John Malkovich. “There was an ice-cream shop on Melrose Avenue and I found it there.”

Jonze — real name Adam Spiegel — has had one of Hollywood’s more varied careers, appearing in films such as Three Kings and The Wolf of Wall Street, alongside his screenwriting and work behind the camera. He directed landmark music videos for Fatboy Slim, Weezer, Björk and others and also co-created the unhinged MTV television series Jackass.

But his background was in publishing. He worked on a skateboard title, Dirt, in the early 1990s, which led him to a stint on the Beastie Boys’ shortlived — but revered — magazine, Grand Royal. Vice magazine “had a point of view”, he says. “That always attracts me, especially in a medium that doesn’t usually have one.” He did not know Smith when he first stumbled upon Vice, but called him in New York and arranged to have lunch. They hit it off and became friends.

“Then a few years later, around 2005, they were doing these incredible stories for the magazine, like trying to buy a dirty bomb in Bulgaria,” Jonze recalls. “I said, just bring a camera! Video online then was just starting to become do-able.”

After that, Vice’s video reports started to flow thick and fast, ranging from the in-depth and serious to the oddball and weird (Vice sent one reporter to cover the Westminster Dog Show, the US equivalent of Crufts, after taking LSD).

Jonze, meanwhile, took on a more formal role as Vice’s creative director, helping it build a video documentary division which would evolve into Vice News. He produced Heavy Metal in Baghdad, a documentary which built on a Vice magazine story about how members of a metal band in the Iraqi capital had been affected by the US invasion.

Smith in the Museum of the Revolution

He also found himself taking a greater interest in current affairs: “I felt like we were inventing a news organisation that was based on us trying to understand the world we lived in, not by being professional journalists but by being curious. The Vice guys came from magazines, I came from magazines but had made some film stuff . . . we were all together trying to work out the language of it and trying to use video to tell stories.”

He got the news bug late. “Before 9/11, when I was younger, I wouldn’t have bought a newspaper,” he says. After the attacks that changed. “I suddenly understood how relevant it was to my life.”

As Vice began to crank up its video output, Jonze was asked by partners of Al Gore if he wanted to be involved in Current TV, the shortlived cable news channel started by the former vice-president.

“I said if I did, I would want to do it with Vice’s editorial staff.” The idea never came to fruition (Current was eventually bought by Al Jazeera, the Qatari-owned media group, which has struggled to attract viewers in the US). “I loved the idea of Vice doing a news channel,” Jonze recalls, hinting that the suggestion was a step too far for Current. “Vice scared the shit out of them.”

We arrive at the restaurant, on the western side of the harbour in Old Havana, and follow the crew up a steep flight of stairs. The air is hot and sticky and the sunshine of earlier has given way to darkening clouds. All the windows are ajar and after a few minutes the heavens open.

I sit at a table with Jonze and Smith, who has ordered a round of daiquiris, and ask Jonze how his work with Vice fits in with his movie commitments. He is clearly part of the Vice “family”. At a recent party to celebrate its 20th birthday, Vice put on a concert that featured performances from, among others, Scarlett Johansson, Pulp’s Jarvis Cocker and Pussy Riot. Jonze and the actor Jonah Hill were also on the bill, jamming a song together.

He has an office at the company’s Williamsburg headquarters and is a regular presence. “He doesn’t have to worry about human resources or headcounts,” says Smith. That responsibility lies with Smith himself, who combines running Vice with negotiating distribution deals for its content — while presenting much of its news programming. When Vice landed a much-sought-after interview with Barack Obama recently for its HBO show, it was Smith who grilled him and chaired a discussion with him and a group of students to talk about the soaring cost of higher education. “Shane represents the company in a big way,” Jonze says. “It’s like making a film. The personality of the person who runs the company really sets the personality of the company.” Smith laughs. “That’s weird.”

Smith founded Vice with friends Suroosh Alvi and Gavin McInnes (Smith and Alvi still control the company; McInnes left in 2008 citing “creative differences”). But Jonze is right to say that Vice has been shaped by Smith’s personality. He is the company’s public face — a mix of showman, salesman and intrepid explorer. His crew clearly want to do well for him and I witness some stressed faces as preparations are made for each shoot.

He grew up a punk fan in Ottawa, inspired by bands like the Sex Pistols and Dead Kennedys, and as Vice magazine took off he fully embraced the hedonistic lifestyle. He has calmed down a bit since then — he is now married with two children — but he clearly thrives on the adrenalin that comes with travelling the world to make television. “The camera is the best passport because you get to see things that no one else sees,” he says.

Cuba seems ideally suited for Vice’s HBO show which focuses on colourful edgy, hotspot stories

In the past couple of years there has been a subtle change of direction at Vice. The magazine that evolved into a digital entity, producing video for the internet and making its money from sponsored online channels, has gone back into traditional media: television. Smith, ordering another round of daiquiris, says it was a necessary move. “There was this digital morass and all these digital companies fighting it out.”

Digital media continues to be highly competitive, particularly among sites that report news or are aimed at the same demographic. Last year, Vice got into a war of words with Gawker, which operates a network of news sites, when a Gawker story alleged that Vice underpaid its employees. Vice hit back in a blog post, accusing Gawker of “garbage, click-bait journalism” and “inaccurate and irresponsible” reporting.

Nick Denton, Gawker’s founder, tells me that Smith’s persona is what holds Vice together. “So much of Vice depends on Smith’s showmanship — and his claim to understand the millennial audience,” he says. He suggests that the company may not be as radical or transformative as its fans in larger media companies may believe. “The commercial success of Vice says more about the insecurity of legacy media than it does about the future of media.”

Vice still competes for online audience with sites like Gawker and BuzzFeed but its move into global television production and distribution means it also has a completely new set of competitors. “We came out of digital and said, our content can go on mobile, online, television . . . ” Smith says. “We’re becoming more of a straight media company.” It is, he adds, “the best time in history to be making content. The mobile carriers, the online platforms and television are all fighting for content [and] they all need it. So if we create it, we can make money.”

He points to an agreement Vice struck with Rogers Communications, the big Canadian media group. The two companies signed a $100m deal in which Vice will build a studio in Toronto and produce programming for Rogers’ phone, internet and television services. It is a model that Smith has taken to other countries. “We get paid to make stuff. We get paid for the advertising that goes with it. Then, if you own [the content] you can take it around the world.”

Producing this content isn’t cheap. “You have to spend the money in the editing room,” says Jonze. “You have to keep editing until it’s good. Creatively, [the editing room] is where you find the story and where you make or break it. You have to feel it: this is good, this affects me.”

Vice is moving to a new building in Brooklyn which will be able to accommodate even more writers, editors and film-makers (it currently employs about 1,500 people worldwide). But this growth raises a big question: what does it do next?

Smith says Vice has three options. It could sell to a larger company and exist within it semi-autonomously (he mentions Ted Turner, the founder of CNN, who sold his company to Time Warner, as an example). It could seek an initial public offering in New York. “There hasn’t been a media company like this to go public in 15 years,” he says. “The markets would love it.” Or it could pursue a third option and stay privately owned. This presents its own problems — mainly, that shareholders with stakes in a company which, on paper, is worth billions of dollars may at some stage want to cash out. “You can be worth $10m but try to buy a cup of coffee with that,” says Smith. “That’s what we’re wrestling with.”

Our next stop is the Hotel Nacional, the grandest in Havana and the site of an infamous 1946 mafia summit that brought together the heads of the major US crime families (fictionalised in The Godfather: Part II). The mafia had extensive interests in Havana in those days — the hotel was one of several that offered casino gambling tightly controlled by the mob and the Fulgencio Batista regime. Now owned by the state, hotels like the Nacional have the WiFi connections required by paquete dealers for downloading US television programming from the internet.

Vice is meeting “Danny”, who deals paquetes, the name given to hard discs packed with media content downloaded from the web. They have enabled Cubans to watch US television programmes that they would otherwise not be able to see: the authorities have turned a blind eye to the phenomenon to the extent that an estimated 80 per cent of households in Havana now have some form of access to US entertainment.

“Danny” takes Smith and his crew into the city to show them the copying operation. “We make daily downloads to keep up to date,” he explains. “America is a country that is always up to date with everything. We also want to be up to date.” Television, he adds, “is enriching and great”.

The next day the crew travels to Guanabacoa, outside Havana, where Smith and Jonze interview Baby Lores. Afterwards, we drive back into Havana to the Museum of the Revolution. Soraya Casamayor, the museum’s guide, gives Smith a tour, starting in front of the “Wall of Cretins”, which features caricatures of recent US presidents. Smith asks what she thinks of Obama (who is not on the wall). “He is trying to bring us together and bring more understanding between us . . . and that is a good thing,” she says. “We’ve been through 50 years of struggle but in the last five months there has been so much hope for the future.”

At dinner that evening I ask Smith if he enjoys the constant travel: he is rarely in New York and says he has run Vice from the road for the past decade. He says he is making up for lost time. “Spike taught me something. When he was between 30 and 40, he was doing all this amazing stuff. But when I was that age I just got drunk. So at the end of that decade he was much further ahead. He said, ‘You have to do the work now, because you don’t have forever.’ That really resonated with me.”

As we talk about what the future might hold for Vice he drops a hint about his plans. “I’m approaching my Bill Gates moment. People say, ‘You don’t want to run a public company’ — and they’re right. It’s not what I’m good at.”

He is considering stepping down as chief executive to free up time to do what he enjoys, he says. “I’m only good at two things,” he continues. “I’m good at making content and I’m good at doing deals. They’re fun . . . but day-to-day business management is hard.” He is vague about the timing but Vice has beefed up its management ranks in recent months hiring, among others, Alyssa Mastromonaco, the former White House deputy chief of staff, as chief operating officer.

He has more expansion plans up his sleeve before he goes. Vice is getting into movie production. It will soon also have its own US cable channel, the result of its deal with A&E.

Would it be the same company without him? As Jonze points out, much of Vice’s personality stems from Smith: while he has been chief executive it has walked the line between commercial success and credibility with its audience. I wonder if he ever worries that Vice could lose the commodity that has made it so sought after: its cool. After all, staying relevant with successive generations of younger viewers and readers is not easy. Think of MySpace, which flamed out after only a few years, or, more recently, MTV, which, after staying relevant for more than two decades, has now slipped into insignificance.

“We’ve never tried to be cool,” Smith laughs, reaching for his glass of wine. “We’ve just tried to make stuff that sucks less than everyone else.”

Matthew Garrahan is the FT’s global media editor. Vice’s Cuba report airs on HBO later this year

This article was amended on May 18 2015 to give Julio Pabón’s correct job title of producer, Vice on HBO