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Marking the fourth big-screen collaboration between actor Leonardo DiCaprio and director Martin Scorsese, “Shutter Island” sweeps you into a twisty, turny, retro mystery drama that deepens and darkens with every scene.

DiCaprio plays U.S. marshal Teddy Daniels, coming in 1954 to a heavily fortified mental institution for the criminally insane located on an island off the coast of Massachusetts. Daniels and his partner (Mark Ruffalo) have been summoned to investigate the bizarre disappearance of one of prisoners, a delusional murderess that butchered her children.

Leonardo DiCaprio stars in the mystery drama, “Shutter Island.”

Where did she go? How did she get out? Do those two creepy docs who run the joint know more than they admit? And what goes on in the spooky, forbidding—-and forbidden—-Ward C, the dark, dank fortress for the REALLY crazy patients?

As the questions start piling up, we also learn that Teddy got off the boat with some heavy mental luggage of his own. He’s tortured by the memories of what he saw, and did, liberating a Nazi concentration camp. And he’s haunted by feverish dreams of his wife, whom he believes perished in an apartment blaze started by an arsonist.

There’s a lot going on in “Shutter Island,” not the least of which is figuring out who’s who, what’s what and why Teddy is really there. It’s an understatement to say that things aren’t quite as they seem.

Working from a script based on a novel by Boston-based writer Dennis Lehane (who also wrote the story that became “Mystic River”), Scorsese paints a moody, ever-intensifying atmosphere of gloom and doom, blurring the lines between what’s really happening and what’s going on in Teddy’s head. It’s an intricately orchestrated descent into madness, leaving you to decide who’s really crazy.

The spotlight belongs to DiCaprio, but several other actors bolster his performance in strong supporting roles. As the institution’s chief psychiatrists, Ben Kingsley and Max Von Sydow give veneers of ambiguous refinement to their characters’ shady, possibly sinister sides. Jackie Earle Haley is a squirreled-away, Ward-C patient with a key to Teddy’s troubled past. Patricia Clarkson has a scene as a wild-looking woman who may, or may not, be the on-the-run murderess.

Some critics have called “Shutter Island” another gem in the Scorsese crown, up there with “Goodfellas,” “The Departed,” “Gangs of New York” or “Cape Fear.” Others are chalking it up as more mess than masterpiece, a jumble of a pulpy detective clichés, unclear plotting, missing pieces, dots that don’t connect, implausible stretches of logic and a preachy jumble of messages about war crime, government secrets and the brutalities of psychiatry practice in the 1950s.

One thing’s certain: Even when it’s over, you’re still guessing. If you like your movies to end wrapped in a cozy, bright, feel-good ribbon, you should paddle toward calmer waters. If, however, you want something that will stay in your own head, bobbing around in the shadows long after the lights come up, “Shutter Island” might be just what the doctor – or the pipe-puffing German psychiatrist – ordered.