The man who reinvented the American action movie chuckles. "Ah," he says, "The Driver. You can't outlive anything any more …"

If The Driver has come back to haunt Walter Hill, then surely it is the good kind of haunting. The 1978 neo-noir thriller, his second picture as a writer-director, has long since outlived the mixed reviews and so-so box-office it earned on its original release. In 35 years it has come full circle from half-forgotten, possibly pretentious, definitely too French B-thriller to earn its rightful place in Hill's storied career.

Nicolas Winding Refn's Drive bears its stylistic imprint like a watermark. The crime movies of Michael Mann, with their professional antagonists-cum-doppelgangers duking it out in a perpetual, neon-lit dark night of the LA soul, could all have been extrapolated entirely from the template of Hill's near-mythic battle between characters so archetypal they don't even have names: the Driver (Ryan O'Neal), the Detective (Bruce Dern) and the Girl (Isabelle Adjani).

The Driver. Photograph: Moviestore/Rex Features

I tell him I think it falls midway between Jean-Pierre Melville's existential hitman movie Le Samouraï, which features a killer, a cop and a girl, and Monte Hellman's existential drag-strip movie Two-Lane Blacktop – lead character names: the Driver, the Mechanic, the Girl.

"Not a bad place to fall at all," laughs Hill, an unfailingly modest recipient of my perhaps overheated praise. We're in the dining room of his large and imposing house on a quiet street in the westerly reaches of Beverly Hills, overlooking a meadow-like garden that slopes down to an azure swimming pool. A compact, burly man with a grey beard and a beautiful deep, smooth growl of a voice, Hill is often reduced to the status of the missing link in action movies between his mentor Sam Peckinpah and his fellow stylist John Woo, but this is to undermine his legacy and patronise his work. He is not in any sense missing – never was, never will be – but he is an important linking figure between generations of film-makers old and, well, less old (he's 72 now), and between old genres and radical new configurations of them.

"We see now," he says, "60 and 70 years later, that John Ford and Howard Hawks are beyond genres. Even so, I always felt that genre film-making was going to be my home, but I also understood that you couldn't go on making them the way they used to do – there's no challenge. If you were just gonna go at it the way the old guys did, then you were going to run up against the fact that they did it better than you ever could – not surprising, since they had invented the genres themselves. My generation found you had to use the old genres in new ways, pull them inside out."

48 Hrs. Photograph: Cinetext/Paramount/Sportsphoto Ltd/Allstar

His first six movies, from Hard Times in 1975 to 48 Hrs in 1982, pull a whole lot of conventions inside out, and offer a concentrated, high-octane dose of bracingly violent action-poetry, one after another; a glorious run for any young film-maker. Hill is also the unofficial conservator of the never quite moribund western genre (who else you gonna call to direct the pilot episode of Deadwood?), perhaps because he considers all his movies to be westerns at heart.

Hill started out as an assistant director on Peter Yates's Bullitt, wrote the screenplays for Peckinpah's The Getaway and John Huston's The Mackintosh Man, witnessed the rise of the movie brats (Scorsese, Coppola, De Palma), the USC mafia (George Lucas, John Milius et al), and the simultaneous sunset years of two great post-war action directors he still admires, Robert Aldrich and Don Siegel. Add to all this his staunch admiration for John Boorman's pace-settingly brutal 1967 thriller Point Blank (whose cinematographer Philip Lathrop shot both The Driver and Hard Times), and his lifelong love of tough-guy Warner Bros director Raoul Walsh – "one of the most perfectly American storytelling stylists, every shot advanced the story" – to whom he dedicated his script for The Getaway, and whose boxing picture Gentleman Jim looms large over Hard Times, and it becomes plain that Hill came of age in the crucible of modern screen violence, just as Hollywood was growing up.

Walter Hill on the red carpet. Photograph: Ernesto Ruscio/Getty Images

"Suddenly the action film was more adult," Hill recalls. "Somehow they were not as corny and as B-picture-ish as they had been in the 1950s. You could make crime movies without any cops, with criminals as protagonists. They were darker, less melodramatic, less held back by the censors, and more influenced by Europe as well."

Hill was on to something new. Certain shots in his Depression-era prizefight movie Hard Times are reminiscent of Edward Hopper and George Bellows; its New Orleans demi-monde is richly detailed; and Barry De Vorzon's soundtrack is soaked in Cajun music and jazz – and yet this is a two-fisted Charles Bronson punch-up movie, in which all blows are painfully amplified and the blood seems awfully real.

"I got the chance to direct from Larry Gordon, great producer – he said I'll pay you writer's minimum and director's minimum, but you'll get to direct. And that was the best deal I ever made, even though Columbia were then financially in dire straits – in those days, you would take any cheque of theirs straight to the bank the minute you got it, in case they went bankrupt before lunch. Charlie Bronson had had a recent hit with Death Wish. We met and he was very … Bronsonian. Afterward he shook hands and asked me why the hell I thought I could direct him. He got a million of our $2.7m budget. My heroes usually have a very talkative foil opposite them or reluctantly alongside them, such as Bruce Dern in The Driver, or Eddie Murphy in 48 Hrs, or James Coburn in Hard Times. I like the kind of dialogue between people who have a mutual goal but very disparate appetites and needs, so that there's always a kind of friction that runs throughout the film. They don't like each other very much, and hopefully the movie supplies a reason for them to achieve a grudging kind of respect for each other. It always surprises me when people call 48 Hrs a "buddy picture" because those guys pretty much hate each other – it's an anti-buddy movie!"

Brewster's Millions. Photograph: Allstar

Hill (like his friend and sometime collaborator Milius, and like myself) was an asthmatic child in the pre-Ventolin era, and was kept out of school for a number of years. "The leading theory about asthma back then was that you had some kind of mental problem," he laughs. "How was it? Well, you know yourself, you feel like you're gonna drown. It turned out not to be chronic and I've not really been affected by it as an adult. I even smoked for a few years, until I came to my senses. But being kept out of school meant I lived in a world of books and radio shows and comic books. And I always wondered if I ever would have drifted into all this if I hadn't gone through all that."

Let's be grateful, then, to asthma, for letting Hill marinate his mind in pop culture. Without it we may never have experienced Hill's brand of cinematic violence and poetics, with its brutal bloodshed and a soundtrack of retro American music. He might never have become the action director who oversaw the movement of horror-movie-style splatter into other genres such as the western (The Long Riders is bloodier than The Wild Bunch), the platoon movie (Southern Comfort) and even science fiction (we often forget that Hill co-wrote and produced Alien). We might never have got to treasure his favourite bad guys, the too-beautiful-for-his-own-goddamn-good, super-loud young James Remar, and mega-twitchy David Patrick Kelly ("Warriors, come out to play-eeee!"), or that gigantic, brain-rattling explosion in Southern Comfort, which I think may be his masterpiece.

The Warriors. Photograph: Moviestore Collection/Rex Features

And now he's the senior statesman, the one doing the influencing: "We all have our influences," he says. "Early in my career, it was said I was very influenced by Peckinpah; now they tend to say I'm more of a Hawksian, but whatever. Sam was tremendously influenced by Kurosawa, and Kurosawa was tremendously influenced by Ford, Ford was tremendously influenced by DW Griffith, and Griffith was tremendously influenced by the novels of Dickens. Now, I don't mean to insert myself in this lineage, I just mean everybody's holding everyone else's hands and everyone's sitting on everyone else's shoulders."

Walter, you don't have to insert yourself in that lineage. You absolutely belong there already.

• The Driver is out now on Blu-ray.