With five such different cinematic visions represented, what do this year’s Oscar nominees for director have in common?

It depends on whom you ask. Kenneth Lonergan, nominated writer-director of “Manchester by the Sea,” links the final five this way: They each “focus on deep connective tissue on a human level, even though they are all very different stylistically and in subject matter,” he tells Variety.

Mel Gibson, director of “Hacksaw Ridge,” invokes the process itself. “What do we have in common?” he asks. “At some point, somebody asked each of us a thousand questions a day and we had to make snap decisions.”

Each shares a fierce inventiveness, necessitated by the time and budget constraints each faced mounting their creatively ambitious projects.

“These movies couldn’t be more different,” points out “Moonlight” writer-director Barry Jenkins. “The movies I like best are the ones where you can feel the curiosity of the filmmaker for the form or the subject matter. The movies I like most ask questions — and these films do that.”

Variety talked with the nominees about the production obstacles they overcame, their behind-the-scenes (and occasionally before-the-camera) MVPs, and the directors who have inspired them.

Damien Chazelle
La La Land” (Lionsgate)
Chazelle, 32, previously received an Oscar nomination for writing “Whiplash” (2014), which won three Academy Awards. “La La Land” is his third feature.

Biggest obstacle: Money was a big hurdle for Chazelle, who wanted to shoot in real locations yet was initially unable to get a tax credit to do so in Los Angeles. “There definitely was talk about other places we could shoot the movie,” he tells Variety.

How you overcame it: “Luckily the producers were very supportive of keeping it in L.A. — but we had to be creative and thrifty, because if there’s a dance number on a freeway, it had to be a real freeway.”

Production MVPs: “I learned firsthand how much a director relies on all the departments functioning as one organization: the choreography, the camera work, the sets, the costumes, the score. They all had to live and breathe together, to feel we’ve created one unified statement. I give credit to those and a hundred other people who worked on this.”

Director heroes: “There are a bunch of them but, for this film, it would be Jacques Demy, Charlie Chaplin, Martin Scorsese, Vincente Minnelli, Stanley Donen, people like that.”

Most personal thing about “La La Land”: “It’s all pretty personal because I was writing about my own experience in Los Angeles. I arrived with big dreams, but no avenue to make them come true. I wanted to capture that feeling of a young artist in limbo.”

What this nomination means to you? “It’s doubly surreal because I’m talking to you from Beijing. But I’m just beaming with pride to see so many people on the team get recognized this way.”

Mel Gibson
“Hacksaw Ridge” (Lionsgate)
Gibson, 61, was nominated once previously for director; he won the award for “Braveheart” (1995), which also took the Oscar for best picture. “Hacksaw Ridge” is his fifth film as a director.

Biggest obstacle: “Getting me to do it. [Producer] Bill Mechanic believed in the story and gave it to me three times. I tend to take time to cogitate about whether I want to spend two years on something, whether it has a good idea I can live with. It’s like a marriage.”

How you overcame it: “It’s like that with everything I direct. Once I decided to do it, we still had to deal with the fact that we were making it independently, with the problems of finding financing and people.”

Production MVPs:
“My producers, Bill Mechanic and David Permut. Bill is as passionate a producer as you can find. He jumps in and gets his hands dirty and bloody — it’s good to have a guy like that in your corner because he’s not just a producer.”

Director heroes: “I grew up watching movies on black-and-white TV, so I watched films by Billy Wilder and Ernst Lubitsch, Frank Capra — films from that golden era of black-and-white films. The ’70s were such a great era, too — Francis Ford Coppola was doing his thing, Sidney Lumet, [Roman] Polanski — I have so many heroes who are directors.”

Most personal thing about “Hacksaw Ridge”: “The act of storytelling is a great thing. With a limited budget, I had to find different ways to cut the cloth to get a lot of bang for my buck. I hadn’t directed a film in 10 years; we’re living in a different era now.”

What this nomination means to you: “I’m grateful for the recognition of the work. Whenever your colleagues recognize your work in a meaningful way, it’s very gratifying and humbling. Hey, I’m an insecure actor, so it’s reassuring to me that people think I’m doing good work.”

Barry Jenkins
“Moonlight” (A24)
Jenkins, 37, previously directed “Medicine for Melancholy” (2008). His work on “Moonlight” already has won almost three dozen awards from festivals and critics’ groups.

Biggest obstacle: “Partly it was with me having a hesitation, being a straight guy, to make a movie where the central character’s sexuality was different from mine.”

How you overcame it: “I decided I would preserve the voice of Tarell McCraney [who wrote the play the film is based on]. If I could do that, I could carry forth.”

Production MVPs: “It would be my producer, Adele Romanski. Once I linked up with her, we moved forward. And James Laxton, my cinematographer. But it’s definitely a collective effort, given the amount of time and budget we had.”

Director heroes: “I’ve always admired Steven Soderbergh, for his curiosity and the variance in the kind of work he does. And Claire Denis and Wong Kar-wai.”

Most personal thing about “Moonlight”: “It’s the main character’s relationship with his mother. When I first read it, I thought, ‘How does Tarell know the things he knows about my life?’ Because it rang so true to my experience.”

What this nomination means to you: “It’s really cool. Tarell and I were both that kid in the movie. But that kid grew up to make a piece of art that’s been nominated for an Academy Award. So people who are from where I’m from can look at what happened with us and be inspired.”

Kenneth Lonergan
“Manchester by the Sea” (Amazon)
Lonergan, 54, has been nominated twice for screenplay: “You Can Count on Me” (2000) and “Gangs of New York” (2002). “Manchester by the Sea” is his third film as a director.

Biggest obstacle: “I didn’t have a lot of obstacles to making the film; it was a pretty smooth path. Writing the script, the challenge was figuring out the structure. I was writing it as a linear story for eight months and it wasn’t working.”

How you overcame it: “Once I thought of the flashback structure, it was the undoing of the logjam.”

Production MVP: “Casey Affleck. I had a great first assistant director and a strong producer in Matt Damon, but the person on the set who was the most supportive everyday was Casey. He focused on helping me get what I needed. He was very focused on scene work and he’s more experienced than I am. He just provided a lot of moral support every day.”

Director heroes: “Martin Scorsese, Stanley Kubrick, Howard Hawks, William Wyler, Francois Truffaut, Vittorio De Sica, Elaine May, Mel Brooks. So many, really.”

Most personal thing about “Manchester by the Sea”: “It’s the idea of the transposition of loss as an experience with things I’ve been through and things I’ve watched friends and loved ones go through. I’ve never been through anything nearly this bad but, when things did happen, I found I had a lot of help. People want to help.”

What this nomination means to you: “It means people like the movie and relate to it. It’s wonderful for your ego and professionally. It’s a little silly, but also wonderful because it’s like a vote of confidence from your own community.”

Denis Villeneuve
Arrival” (Paramount)
Villeneuve, 49, whose “Blade Runner 2049” will be released this year, directed foreign-language film Oscar nominee, “Incendies” (2010). “Arrival” is his eighth feature.

Biggest obstacle: “It was a huge movie; I was struck when I read the screenplay by the scope. But we had to do it with a lower budget and achieve this scope with less money. The challenge was to protect the scope and I took on the film with the condition that we put all the money in front of the camera.”

How you overcame it: “It took a lot of creativity in production design to find a way to tell the story in the most economic way. We put a lot into creating the interior of the spaceship, to inspire the actors and the cinematographer.”

Production MVPs: “Each movie has its own heroes but, for me, Amy Adams was the soul of ‘Arrival.’ She was a source of inspiration and a muse. And Joe Walker, my editor — he made sure the circular structure worked and found the right equilibrium between the puzzle and the emotional journey.”

Director heroes: “I was raised with Steven Spielberg as a kid, and then I fell in love with Ingmar Bergman; I’m a
big Bergman fan. Ridley Scott was a big source of inspiration, and Stanley Kubrick.”

Most personal thing about “Arrival”: “For me, the design of the aliens and their language was something I personally supervised. The relationship between Amy and her daughter is also something I’m close to.”

What this nomination means to you: “It means the world; it is the biggest honor ever in my life. I came from Canada to start working in another country. To have other directors recognize my work is like being welcomed into a big family.”