On display in Robert Zemeckis' ImageMovers production studio, near Santa Barbara in California, is a souvenir from somewhere else on the space-time continuum: a skateboard, only it's hot pink, has no wheels, and appears to be floating in mid-air, a few inches off the bottom of its display case.

It's a hoverboard, a prop from Back to the Future: Part II, the film in which Marty, played by a fresh-faced Michael J. Fox, travels via DeLorean to a cartoonish then-future of flying cars and self-lacing sneakers. In 1989, when the film was made, Marty's temporal destination must have seemed unthinkably far off: October 21, 2015.

Just over 30 years since the first Back to the Future, the "comedy-adventure-sci-fi-time-travel-love story" that gave his career a 1.21 gigawatt jolt, Zemeckis seems pleasantly mystified by the enduring phenomenal appeal of the franchise.

"I was just hoping we'd break even!" he says, of his initial aspirations. "To this day I don't understand why that film took off. But then again, that's not the filmmaker's job, is it? If I knew that secret then I'd be doing it all the time."

2015 may have not presented real, working hoverboards, but it did offer up a Blu-Ray rerelease of the Back to the Future trilogy, several cast reunions, a behind-the-scenes book (We Don't Need Roads), a fan-made documentary (Back in Time) and countless Back to the Future-themed think pieces timed around October 21, which certain corners of the internet had dubbed "Back to the Future Day".

"The fact that I made a film that continues to resonate, however many generations later, is an absolute honour and thrill," says Zemeckis. "But there's only one downside to all that. It reminds me of how old I am."

Zemeckis' latest is Allied, a stylish, golden-hued romantic thriller that's been described as Casablanca meets Mr and Mrs Smith, starring Brad Pitt and Marion Cotillard as spies in French Morocco in 1942. Before screening a few unfinished scenes for an all-male group of visiting journalists at ImageMovers, Zemeckis encourages everyone to get in touch with their feminine sides.

Though a love affair is laced through his multiple Academy Award-winning film Forrest Gump, Allied is new cinematic territory for Zemeckis. "I think I've matured into a story like this," he says. "In keeping with this theme of feminine sides: I think why directors are attracted to material is exactly like love affairs. There's no real science to it."

If Back to the Future was an audacious blend of disparate genres, it's also true of Zemeckis' career as a whole. His films encompass the rollicking adventure of Romancing the Stone (which actually pre-dated Raiders of the Lost Ark), the Hitchcockian dread of What Lies Beneath, the serious contemplation of science and faith in the sci-fi drama Contact and, in Who Framed Roger Rabbit, a juggling act between the sensibilities of Looney Tunes cartoons and the LA noir of Chinatown.

"I don't have a bucket list of genres that I'm checking off," says Zemeckis. "It's not by design. However, maybe – and I swear that it's subconscious – there might be a slight arrogance in it: Oh, let me see if I can pull this off. Or, I've never done this before … Or maybe a more generous way of saying it is – I like to stretch. This'll get me up in the morning. I think it would be horrid when I try to imagine doing the same thing over and over again, because I love all forms of film."

Zemeckis first met his Back to the Future co-writer Bob Gale while studying at the School of Cinematic Arts at the University of Southern California, bonding over a shared love of mainstream Hollywood cinema (and a distaste for the fashionable French New Wave). In his final year, Steven Spielberg, only five years older than Zemeckis but already industrially influential, took an interest in the aspiring director's work. Zemeckis still recalls the excitement of showing his own student film at Universal Studios at Spielberg's invitation.

"It was heady stuff!" he says. "I came in with my print under my arms, and handed it to the projectionist who threaded it up, and the two of us sat in this little screening room. And you sit there and you think, oh, Alfred Hitchcock sat right here in this chair watching his dailies for Psycho…"

Spielberg was instrumental in Zemeckis' early career, even lending a hand with Back to the Future script rewrites. At the Forrest Gump-dominated Academy Awards in 1995, it was Spielberg who handed Zemeckis his best director Oscar.

Beyond those films, Zemeckis has consistently pushed for technical innovation in visibly effects-laden films. Who Framed Roger Rabbit, Forrest Gump and Back to the Future: Parts II and III all tested the limits of various movie technologies – human actors interacting with cartoon characters, Tom Hanks shaking hands with John F. Kennedy, Michael J. Fox sharing the screen with Michael J. Fox.

Some performers are flustered by Zemeckis' effects-centric approach. "All of a sudden they walk into a blue-screen void and they say, 'Wait a second, what's this going to look like again?'" he says. Meryl Streep, for one, complained bitterly of the filming process on the fantasy comedy Death Becomes Her.

"You stand there like a piece of machinery," said Streep of her ordeal. "It was like being at the dentist."

Streep's comments get a chuckle out of Zemeckis. "You know, I always find it interesting when actors complain about having to do scenes that are visual effects-driven, because a close-up is the most powerful visual effect. Usually it's an actor looking at a piece of tape. It's the most unnatural thing that an actor can do. And yet we do it all the time, and it's one of our most powerful tools."

In any case, Zemeckis' recent films, next to some of the more self-consciously showy effects of his past work, make use of digital technology more surreptitiously. There was plenty of digitally enhanced spectacle of his 2015 film The Walk, about the French artist who tightrope-walked between New York's World Trade Centre towers in 1974.

"Half the shots in The Walk are mo-cap puppets, digital avatars – and nobody knows!" Ticket sales weren't helped by early reports that the film was so physiologically convincing that the movie induced vertigo and vomiting, but Zemeckis regards The Walk as the pinnacle of his career to that point. "Everything that I did in my entire career, in film technique and effects design, prepared me to make The Walk. Years, decades of knowledge prepared me for that."

This time around there are 600 special effect shots in Allied, which – if he's done his job right, Zemeckis says – "hopefully, you won't, you know, 'see'."

"It's just using the tools that we have," he says. "It's a technical art form. All it is, is illusion."