Sam Rockwell has over 70 films, dozens of TV appearances, multiple stage credits and zero Oscars to his name, and some people are getting a little upset about that. Nomination demands from critics and film writers began back in 2009 with his virtual one-man show opposite himself as isolated astronaut(s) Sam Bell in Moon.

You get the feeling he’s always been something of a one-man show, at least in his head. He lived there a lot as the only child of actors who divorced when he was five. Rockwell was raised mainly by his dad in San Francisco, but spent a month each year with his mom in New York, where he made his stage debut playing Humphrey Bogart in an East Village improv comedy sketch she was starring in. It also involved hanging around her crowd of friends, dope-smoking, girl-kissing and singing telegram delivery. All of which made going back to school and basketball on the West Coast a little dislocating. “It was like being an alien.” It might also partially explain the sense of loneliness that often lurks beneath even his most antic characters.

Nevertheless, it was a life he romanticized, and in 1990 he became a struggling New York actor himself, studying with famed acting coach Terry Knickerbocker while working as a busboy, bicycle burrito-delivery guy and assistant to a private detective to pay the bills. (Why has no one written that movie?)

His breakthrough came in 1996 with Tom DiCillo’s Box of Moonlight, playing an eccentric man-child who dresses like Davy Crockett and lives in an isolated mobile home. It put him on the map – the indie map, anyway – and in 1998 alone he had three films at Sundance: He played a romantic outcast in Lawn Dogs, an inept criminal in Safe Men and an eager apprentice assassin in Jerry and Tom. The New York Times cited the triple-header as evidence of his range, even if it was a range of “rogues, crooks and oddballs.” Colleagues described him as the acting equivalent of a Swiss Army knife, and if the Academy didn’t notice, casting directors did. Thus began Rockwell’s history of frenetic line crossing – from indie to studio films, supporting roles to (occasional) leads and just about any genre invented.

After small but standout roles in The Green Mile and Galaxy Quest in 1999, he got the lead in 2002’s Confessions of a Dangerous Mind thanks to director George Clooney, who fought hard for him when studio execs wanted a bigger name. The Times wrote, “The film’s Chuck Barris, Sam Rockwell, does a mambo in his head between geekdom and desperation, and Mr. Rockwell does a dazzling job of conveying the seething confusion beneath his character’s dazed amiability.” The next year, he was equally enthralling as an exuberant, all-in con man opposite Nicholas Cage in Matchstick Men, a performance Entertainment Weekly said made him “destined by a kind of excessive interestingness to forever be a colorful sidekick.”

Putting aside the implications of that assessment for a moment, if you’re going to be accused of excessive anything, “interestingness” ain’t bad. He went on to prove it in The Assassination of Jesse James, giving unusual depth to the simple-minded Charley Ford, and then as a has-been basketball coach in The Winning Season. The Hollywood Reporter cited several fine moments in that under-seen film. “His character stands in for many people who, after high school glory in sports, find themselves lost in an adult world no longer interested in long-ago exploits. Rockwell demonstrates he has what it takes to play those bitter disappointments with some real emotions.” And then there was The Way, Way Back, a lighter but no less brilliant turn as the offbeat manager of a decrepit water park. The Atlantic’s film critic Christopher Orr wrote, “It’s Rockwell’s Owen – an overgrown boy in a movie full of regressing adults – who contributes most to the film’s air of compassionate whimsy. If this role, one in a series of sneaky-good performances that Rockwell’s been delivering for years, doesn’t finally earn him the recognition he deserves, I’m not sure what will.”

Rockwell’s a guy who brings lightness to villains, accessibility to nutjobs and a melancholy, dark side to heroes. He also brings complete commitment born of a ceaseless work ethic and the desire to better any project he’s involved in. His Iron Man 2 director Jon Favreau relies on that. “You’re not getting the guy phoning it in on the big ones and then being an artist on the small ones. He brings his game to all his roles.” ‘Jesse James’ co-star Jeremy Renner told The Guardian UK, “He’s completely fearless as an actor. There’s a real trap with some actors where they play so oddball they’re not accessible. But Sam finds a way home, every time. And you can’t wait for him to come on the screen again because you just don’t know what’s going to happen.” He’s an artist who’s willing to take risks, and that makes him a blast to watch on screen in any capacity.

Taking risks is something Rockwell thinks the business could do a bit more of, but doesn’t, attached as it is to financial success. He’s laughed that directors finally get to him after they’ve gone through all the unavailable leading men. He acknowledges he’s not your typical star or genre headliner. “I don’t know what the hell my category is.”

If he doesn’t, Salon might. In a 2013 interview, Rockwell’s expressed passion for 1970s American cinema led the magazine to speculate that he could’ve been a major star of that decade. “Nowadays you need classic good looks and a chiseled physique to be a Hollywood leading man. Compare that to the days when Dustin Hoffman and Jack Nicholson were the biggest and most honored actors in the business.” That brings up the frustrating possibility that we’ve been denied some really interesting movies, which in turn brings up his latest, Three Billboards Outside Ebbing, Missouri. His supporting role opposite Frances McDormand as a racist small-town cop is renewing calls for an Oscar nomination.

“It’s Sam Rockwell who really punches through the ensemble with a dramatic arc and a reminder that the journeyman actor can be one of the best tools in a director’s arsenal,” wrote Variety in an early review. “As hateful Missouri law officer Jason Dixon, he’s clearly a few bricks shy of a load, a simpleton who is the product of his limited environment. But he’s by no means a caricature. Rockwell deserves supporting actor recognition for the emotional journey he’s able to convey with his character.” Writing from the Venice film festival, their film critic Owen Gleiberman went on to praise Rockwell for “daring to make himself gnarly and dislikable, only to undergo a transformation that the actor, mining his moonstruck ability to win laughs in even the most disturbing situations, makes spiritually convincing.”

It may be tough to describe what makes Rockwell such a riveting shape-shifter, but he likes a description of acting he once heard from Gary Oldman (another actor Hollywood took way too long to recognize with an Oscar nom): “It’s kind of like you’re taking a snow globe — you being the vessel, the snow globe — and you’re shaking up all this stuff that’s inside you from your past, and you have to kind of explore that again.” The past 29 years have proven Rockwell has an Atlas-sized globe to work with, and we hope he keeps roiling it. Whatever may fall out is far more worthy of anticipation than any statuette.