“She’s a girl with a problem,” Roman Polanski says on the director’s commentary of Repulsion, speaking as efficiently and abstractly as he directs. He’s describing Catherine Deneuve’s Carole, a stoic young woman of ineffable beauty and disintegrating mental health who is harassed by some boorish men, as women often are, and then kills them, by bludgeon and by straight razor. Polanski delves deeper into the ruinous mind of a damaged, desecrated woman than any other director had done before, excavating the contradictions and afflictions of her undefined “problem” and erecting a nightmarish world that reflects her point of view. His distant yet intimate approach became the locus classicus of a new psychological aesthetic, one that Polanski himself describes aptly: Girl With A Problem movies.

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Carole, a Belgian manicurist, lives with her sister Helen (Yvonne Furneaux) in a Kensington flat. Carole’s a strange girl with a tendency to drift off, leaving her body behind like an immaculate husk. Yet despite her distance, she seems to accrue horny male acolytes, who are apparently unconcerned with her near-catatonic state. Carole is fiercely uncomfortable around men, and appears revolted even by the objects they use in quotidian life. She shirks away when they try to touch her, and tries to smother her head with pillows as Helen and Helen’s boyfriend, Michael (Ian Hendry), loudly make love in the room beside her, as the whole apartment quivers.

As Bill Horrigan puts it in his accompanying essay included with the Criterion Blu-ray, “The overriding acoustic effect is one of invasiveness, of unwelcome sounds overheard, the centerpiece being Helen’s orgasmic aria penetrating the thin walls of Carole’s bedroom, sexuality itself loudly proclaimed.” Men invade her personal space and leave their stuff around her apartment, like shedding flakes of dead skin. Michael in particular has an annoying habit of leaving his toothbrush and razor in Carole’s glass; she removes his toothbrush apprehensively, as if picking up something dead and decaying, the way her sleazy, sweaty landlord later picks up the dead rabbit Carole left out to rot. She eventually uses that icky razor to slash that icky landlord to ribbons. This sexual anxiety, and the subsequent discharge of violence sets a precedent for subsequent Polanski films, like Rosemary’s Baby.

Repulsion, which turned 50 this year, wasn’t supposed to be a classic. Polanski took on the project with co-writer Gérard Brach to help earn funds for his still-gestating Cul-De-Sac. Shooting on the quick and cheap necessitated some thrifty bravado, at which Polanski is unsurpassed: He laces the film with disquieting noises, the banal sounds of daily life amplified severely so they now sound like the clamors of a nightmare. (David Lynch would employ similar tactics in Eraserhead less than 10 years later; his film shares many aesthetic and thematic traits with Repulsion, but is decidedly masculine.) Expounding on the shoestring classic Carnival Of Souls (1962), Polanski uses heightened sounds and simple, articulate camerawork to compensate for budgetary restrictions. A lot of the traits and tropes of the aesthetic were engendered out of necessity, coalescing into the oppressive atmosphere that permeates Repulsion.

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That certain ineffable quality pervades and defines the Girl With A Problem aesthetic. This psychological unraveling manifests in dilapidated architecture, claustrophobic atmospheres, and isolation. Hallways appear long and narrow, walls leaning inwards, ceilings slanting down, and windows awash with sallow light. People often liken films with this kind of feeling to “Polanski’s early movies,” a description of the same nebulous breed as “Lynchian” and “Kafkaesque” in its vagueness. But you know what someone means when they say it; you know the kind of solipsistic claustrophobia they’re thinking of. This distinct feeling differentiates Girl With A Problem movies from other psychological horror films, like Polanski’s own The Tenant or Kubrick’s The Shining (which presents the point of view of multiple characters instead of just one). It has to do with the perspective these films take, and of course with their femininity. They exist within immersive, insular worlds woven out of the shreds of their protagonists’ psyches, untethered from reason and logic.

“Our perceptions are shaped by the sum of our visual experiences,” Polanski said, after reading R.L. Gregory’s Eye And Brain: The Psychology Of Seeing. “We see far less than we think because of past impressions stored in our minds.” Repulsion seductively pulls us into the mind’s eye of Carole from the opening shot, a sustained close-up of her flittering eye (shades of Vertigo). Eyes are the windows to madness in the Girl With A Problem films, which take place in fantasy lands that reflect their protagonists’ anxieties. The “problem,” whatever it may be, spills out like blood from a head wound, washing over the film realm, seeping into the crevices and growing like so many weeds. This is achingly evident in Queen Of Earth, which director Alex Ross Perry has called a “broken woman” movie, citing its predecessors as Interiors and The Bitter Tears Of Petra Von Kant, as well as Polanski. Catherine (Elisabeth Moss) and her best friend Ginny (Katherine Waterston), retreat to a house in the woods. Perry depicts the world as Moss’s Catherine sees it: Warped and wicked, not unlike Carole looking at her own face gleaming off the curved side of a tea kettle. Channeling Polanski, Perry shoots Queen Of Earth in discomforting close-ups, smearing mascara around Elisabeth Moss’ eyes so they look sunken in, eroding holes into which the rest of her face may soon sink. Her mind corrodes and her world comes apart, and we feel as though we’ve fallen into the hollows of her eyes and into the void behind. In Repulsion, as Carole’s mind continues to split into increasingly jagged shards, so do the walls in her apartment crack and crumble. Her decaying sanctuary, and the decaying rabbit around which now buzzes a flotilla of flies, spawned one of the most immediately identifiable traits of the Girl With A Problem movies: a slowly rotting perishable. In Queen Of Earth, Catherine keeps a salad beside her bed, the wilting, withering greens emblematic of her decaying mind. Neither of these metaphors is very subtle, but that’s part of what makes them so unsettling: Both Carole and Catherine are struggling with pretty obvious mental illnesses, yet no one seems to notice, or if they do, they respond with irritation.

Girl With A Problem movies are also penetrated by a deep, throbbing sensation of sexual anxiety and identity, women struggling with their desires in a world that suffocates them. Before Repulsion and the advent of New Hollywood, American filmmakers had limited options for depicting sexuality. (Hitchcock found clever ways around this, though his was exclusively a male perspective.) Polanski, one of the cinema’s preeminent cynics, rose to prominence at a time when sex swelled on screen and moral apprehension dissipated. Carole abhors being touched by men, and assuages that discomfort with violence.

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Darren Aronofsky’s Black Swan, a lustful, fetishistic film, takes the brooding horrors of Repulsion and mingles them with the tragedy of The Red Shoes, a combination that seems, in retrospect, so obvious you have to wonder why no one thought of it earlier. Ambitious ballerina Nina (Natalie Portman) lives under the tyrannical love of her mother (Barbara Hershey). The pressures and stress of life begin to eat away at her; the way Carole’s wall cracks, Nina’s body begins to fall apart. The way hands reach out of the halls for Carole, the hands of a beautiful rival (Mila Kunis) reach out for Nina, caress her, cajole her. But because it’s just a fantasy, it only tenses Nina more, and her body can’t take all that mounting pressure. Carole reacts to the advances of men by stabbing and clobbering them; Nina responds to a repressed sexual awakening by stabbing herself with a shard of mirror.

For whatever reason, most of these movies that draw influence from Polanski’s Repulsion primarily feature women who love and have sex with other women, the implications of which could fuel an entire book. As with Black Swan, which features a fantastical scene of Portman and Kunis in the thralls of passion as Hershey pounds in vain on the door, David Lynch saturates Mulholland Drive, his poison valentine to Hollywood, with sexual tension and the dread of rejection. The steamy sex scene, which feels culled from an erotic fantasy rather than anything rooted in reality, is revealed to actually be an erotic fantasy. Robert Altman’s fever-dream drama 3 Women and Ingmar Bergman’s Persona give us less assurance, slipping so far into sex-steeped delirium we never find out way out. All of these movies depict living worlds transmogrified by the anxieties of their female progenitors.

You can’t watch or discuss Repulsion and its sexual anxieties without bringing up, and possibly dwelling on, Catherine Deneuve’s physical flawlessness, from that impossibly lush hairdo to the subtle curvature of her chin and her perfect complexion. “I hate doing this to a beautiful woman,” Polanski’s cinematographer Gil Taylor said on set, after shooting a particularly wrenching scene. But her beauty is her most immediate and objective character trait: Viewers don’t want to see bad things happen to, or because of, a beautiful woman. And yet Polanski and Deneuve play off of the perverse desires of (straight male) viewers, who probably have more in common with the creeps doting on Carole than they’re willing to admit.

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Jonathan Glazer goes a step further in his beguiling Under The Skin, in which a woman (or, rather, an alien wearing the fleshy contours of a woman) harnesses her sexuality and beauty as a weapon so she can harvest men. Glazer expounds on Polanski’s cinematic language the way Brian De Palma expounds on Hitchcock’s by casting Scarlett Johansson, the only woman to be voted the sexiest in the world by Esquire twice (what an honor!), as the man-devouring creature. He collates naturalism and surrealism: Using hidden cameras, Glazer recorded the unscripted interactions between Johansson and native Glasgow men, as well as the men lured, and lulled, by a naked Johansson into that tar-pit void where ambiguous viscous fluids suck the life out of them. Johansson’s alien dons the persona of a glacial woman who appears distressed, asking for directions, a creature feigning a problem only for a genuine problem to arise later on, when it/she grows curious about humanity, gazing upon the naked flesh of her guise in the mirror. The most cryptic, Stygian insinuation of the film occurs when the alien is thwarted and humanity saved by a thuggish rapist who immolates Johansson. It’s the ultimate uncomfortable irony in a film inundated with uncomfortable ironies.

Ultimately, none of the women in any of the aforementioned movies comes away from her ordeal unscathed. Some end up dead, some cease to exist, as if they dispersed into the ether. Carole is carried back to reality—by a man, no less—to face the horrors from which she’s been hiding. “I must get this crack fixed,” she says earlier in the film. But Carole never gets that crack fixed. None of the girls with problems do.