There isn't another video game firm in the world like Rockstar Games. Founded in 1998 by Dan Houser and his brother Sam, it has been responsible for some of the most fascinating, successful and controversial video games ever, including the groundbreaking Grand Theft Auto series (120m sales and counting) and the vast wild west adventure, Red Dead Redemption.

Yet little is known about the inner workings of this multinational publisher and developer. The company does not attend industry events such as the huge E3 exhibition in Los Angeles, and unlike most execs in this industry, the Housers rarely court publicity for themselves.

I meet with Dan in New York, at an astounding Lower East Side apartment owned and rented out by the horror film director Marcus Nispel. Rockstar is in the process of introducing the press to its latest title Grand Theft Auto V, and clearly wants to make an impression – hence the venue, and hence the presence of Dan Houser for a handful of interviews. He is, it turns out, affable, passionate and hugely eloquent about game design and culture. He also looks tired. When I ask how far in advance the team starts planning its next games, he laughs wearily. "We don't start until the very end of a project. At the moment, the thought of even doing another Grand Theft Auto is so appalling – we've got so much work left to do to finish this one. It's overwhelming!"

It was Sam who kicked the Rockstar story off. In 1996 he was heading the interactive division of music label BMG, which was experimenting in the new-fangled games business. Sam had heard about developer DMA Design, based in Dundee, which was working on a crazy crime action game named Grand Theft Auto, in which players drove around a city, robbing banks and fighting cops. It had 2D graphics and looked dated compared to everything else. "What did I think when I first saw it?" says Dan. "Well to begin with I had the natural reaction – 'what is Sam talking about?'! The code would literally run for 10 seconds and crash. But when you started playing you understood the magic."

Released in 1997, Grand Theft Auto was a modest success, but BMG was losing money and desperate to get out of games, so it sold its interactive division to Take Two for a paltry $9m. Take Two invited Sam Houser to start up a new publishing arm in New York; Sam agreed, on the condition he could do it under his brand, Rockstar. The next release was the seminal Grand Theft Auto III, which switched to modern 3D polygonal graphics, added a licensed CD soundtrack and became the biggest game of 2001. Subsequent sequels, including the 80s-obsessed GTA: Vice City and the darker GTA IV, pushed boundaries of game design and structure.

Dan Houser is a lead writer on all Rockstar titles. He works with a small team, including Rupert Humphries (son of comedian Barry Humphries), to create the huge scripts and interlocking stories that give shape to the company's giant open-world titles. At first, the studio was hugely influenced by movies such as Brian de Palma's Scarface, Reservoir Dogs and Boyz N the Hood, but as the GTA series went on, Houser says they began to find their own voice.

"You know, with those first 3D games, we were trying to make something that had the aspirations to be like a movie," he says. "I don't want oversell this, but by GTA IV, we wanted to try to find something that could be better than movies in a way – more alive and more vibrant. It was time to move on and do our own thing."

GTA V, due out next spring, is the sprawling and impressively intricate realisation of that ambition. The game is set in Los Santos, Rockstar's Los Angeles, and features three very different criminals seeking to pull off a series of daring heists. The world is vast, taking in a whole city as well as mountain ranges, deserts and outback towns. Characters will have unprecedented freedom – flying helicopters, scuba diving, even playing sports. It is astonishingly ambitous. How does the team begin such a massive creative project? "For us, it starts with the characters," says Houser. "The story is always driven by the characters – it's always got to feel like someone you want to be propelled through the game world with. Then we'll find a cool, interesting and amusing cast to juxtapose them with, and make sure we've got a good range of types. If the process feels organic to us then we're heading in the right direction."

For Dan, the direction now is toward something entirely new. We talk a little about how, in the digital age, interactive and linear content are merging: families and couples now share games in the same way they once shared television. He sees GTA V as at the vanguard of a new entertainment era. "This game, if we get it right, will be a step toward some kind of organic living soap opera," says Houser. "You have these three characters and they're all living when you're not with them. What that means, we don't really know yet, we're only getting it working for the first time. But it feels to us something powerful."

Throughout the 90s, the Grand Theft Auto titles were targeted by tabloids and rightwing pressure groups for their depiction of casual violence. It all exploded in 2005 with the release of Grand Theft Auto: San Andreas; Sam Houser and several members of the development team were interrogated by the Federal Trade Commission when an explicit sex scene, which had been cut from the game but left hidden in its source code, was discovered by hackers. A year later, the company was let off with a warning, but the experience left its mark.

"It was draining and upsetting – a tough time in the company," says Houser. And that's all he'll say, but the emotion is there – and in some ways this terrifying period seems to have shaped Rockstar's relationship with the press, and with the outside world. He sighs heavily.

"The massive social decay that we were supposed to induce hasn't happened. So in that regard, a lot of those debates that used to go on, they're not such a big deal now. We never felt that we were being attacked for the content, we were being attacked for the medium, which felt a little unfair. If all of this stuff had been put into a book or a movie, people wouldn't have blinked an eye. And there are far bigger issues to worry about in society than this."

But the brothers' reluctance to go in front of the media is about more than their past experiences, it's about how their company works. "Our skill has been in creating that environment where hundreds of people can flourish," Houser says. "It is far better than my ability or otherwise to write, or Sam's to tune games – creating the environment and working together is what makes us proud. Journalists are obsessed with biography stories, but it's not relevant to us. It's always been about the company. Every different person here has their own weaknesses, their own hang-ups but together we produce magic."

It sounds like company PR, but Houser is earnest and honest. The team is everything, Rockstar is a gang; and its relationship with the world is defined by that. He is also unexpectedly self-effacing. Towards the end of the interview I ask him what he'd be doing now if GTA had failed. He leans forward, opens another Coke and thinks for a second. "I can't answer your question because I've always done this," he jokes. "My family thought I was a loser, so my brother gave me a job and I've spent the last 15 years trying to justify it. I've done that to the best of my ability – and it's been enormous fun."