The Web site for the home-entertainment company Criterion has a feature in which well-known fans list their favorite works from the collection. Unsurprisingly, given that Criterion tends to attract obsessives, there’s an emphasis on the act of rewatching—references to having seen a film “forty times” (the actress Brie Larson, “The Game”) or “once every few years” or “endlessly” ­or “again and again” ­ or “over and over again” or, in the case of the playwright Annie Baker and Ingmar Bergman’s “Fanny and Alexander,” “more times than I can count.” As the fans’ comments reveal, motives for rewatching films are diverse, even polar. On the one hand, there is proven pleasure; on the other, the quest for illumination—a quest that often fails. “Something to do with Heidegger?” the writer Geoff Dyer wonders in his note accompanying Terrence Malick’s “The Thin Red Line.” “Darned if I know, but happy to watch repeatedly in the hope of finding out.”

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The films of Alain Resnais have long been a magnet for such fruitless devotion. Resnais was a director of documentaries about art, whose turn to fiction filmmaking coincided with the breaking of the New Wave. But his films had more in common with the art-house conundrums of Antonioni, Fellini, and Bergman, as well as the agitated, modernist directors of the Left Bank school and the practitioners of the nouveau roman—movements associated with the use of flashbacks and repetition. Resnais continued to make films until his death, in 2014, many of them in the genres of farce and the musical, but he remains best known for his followup to “Hiroshima Mon Amour,” “Last Year at Marienbad,” a collaboration with the leading nouveau romancier Alain Robbe-Grillet, about a man and a woman who may or may not have been together in a German spa town (which may or may not have been Marienbad) the previous summer. On the Criterion site, the director William Friedkin claims that he has seen “Last Year at Marienbad” at least twenty times over half a century and still doesn’t understand a single scene. Now Criterion has come out with Resnais’s subsequent film, “Muriel, or The Time of Return,” which has been baffling people since it showed at the first New York Film Festival, in 1963. Eugene Archer, who was covering the festival for the Times, wrote that almost everyone agreed the film “was impossible to understand after a single viewing.”

In his 2008 book, “Have You Seen . . . ?” the film critic David Thomson wrote that nearly everyone “will tell you how many times they saw the picture—and how many more times are still needed.” But this isn’t quite true. Over the years, many people have declared that once is enough—or would have been. “I have seen the film twice, and expected to see more in it the second time,” Susan Sontag wrote, in a review in Film Quarterly. “I didn’t.” You might assume that the author of “Against Interpretation,” an essay that sought to displace hermeneutics with “an erotics of art,” had no business trying to “see more” in a film that hadn’t given her pleasure. But the problem surely lies with “Muriel.”

The film concerns Hélène (Delphine Seyrig), a widow who sells antiques from the apartment she shares with her stepson, Bernard. One day, she receives a visit from Alphonse, an old lover, and his mistress, whom he calls his niece. Boulogne, where Hélène lives, was partly destroyed in the Second World War, and then reconstructed, and now feels like two cities. Bernard has recently returned from Algeria, where, as a soldier, he may or may not have tortured a girl named Muriel. The film’s every move cues the viewer to look for meaning and significance. The editing disrupts continuities of time and space, and gives a prominent position to obscurely freighted closeups; the modernist score has suspense-thriller trappings (crashing cymbals, heightened strings). There’s a lot of strange, sudden laughter, and the dialogue is full of non sequiturs and talk conducted at cross-purposes.

My own conclusion, after a couple of restless viewings, is that the desire for illumination is just what Resnais is seeking to frustrate. He’s imparting a mood, not transmitting a message. Crudely put, he wants the viewer to feel as uneasy about his film as his characters do about post-war Boulogne and colonial Algeria. The literary critic Yvor Winters might have derided the project as relying on “the fallacy of imitative form,” but you’d be hard-pressed to achieve the same disorienting effect in another way. The Resnais rewatcher’s only hope is that “Muriel,” while refusing to become less cryptic, will yield other pleasures. As Penelope Gilliatt advised, “You may have to go to the film at least twice, as I did, before the warmth of it seeps through.”

“Muriel” is clearly a special case, but it also invites broader questions about what happens when we return to a movie: Is rewatching a compliment or a betrayal, a tribute or a travesty? In an attack on Resnais and others that appeared in The Atlantic, in 1964_,__ _Pauline Kael—Gilliatt’s future fellow-film critic at The New Yorker—presented Gilliatt’s statement as an object for ridicule. Kael didn’t like Resnais, and she wasn’t any keener on the idea of rewatching films. (In May, “Pauline Kael and the never rewatch” was the title of a lively message thread on Reddit.) “Would you rather I studied a movie?” she asked an interviewer, in 2000. “I like it best on the first viewing because it’s got suspense and excitement. . . . I come from a generation that saw movies once. When 16-mm. projectors and film societies started to be popular, and, more recently, when movie lovers got videos, they began to poke over the movies endlessly. I think that violates people’s first reactions; they become scholars of movies instead of people who respond to what they see.” (A friend of Kael’s recalled that she actually forbade him from accompanying her to “The Virgin Suicides” because he’d seen it already; he had to go to “Chicken Run.”)

Kael was understandably bewildered by the fact that Orson Welles had screened John Ford’s “Stagecoach” forty times while he made “Citizen Kane,” particularly as the immersion in Ford’s realism nowhere manifests in the Expressionist “exaggerations” of Welles’s film. As Welles told Peter Bogdanovich, the first day of production on “Citizen Kane” was to be his first time on a movie set; to train himself, he would invite technicians and studio department heads to watch Ford’s “classically perfect” film with him, asking them questions as they rewatched. He called “Stagecoach” a “textbook” and described the experience as “like going to school.”

The rewatching impulse originates in humility, a willingness to learn or change. At the very least, you need a scintilla of self-doubt. The director Whit Stillman told me that he often believes that he has seen a film “ ‘enough times,’ but if I then do watch it again I’m surprised at what a new and important experience the new viewing is.” When Geoff Dyer introduces screenings of Tarkovsky’s “Stalker,” the subject of his granular study “Zona,” he often expects to leave after fifteen minutes but finds himself staying “for a bit longer and a bit longer” until he has sat through the whole film once again: not only are there “new things to notice” but he finds it “more moving than ever.” By contrast, in her first article for The New Yorker, Kael wrote that catching an old movie on television allows us to confirm our own “rightness.”

For Thomson, the effect that rewatching has on films themselves deserves further scrutiny. In an article published in 1977 that begins “ ‘Red River’ was the first film I saw twice,” Thomson used Howard Hawks’s Western to reflect more broadly on how movies change along with us. He said that he had revisited “Red River” to “calm myself” and “even to fashion myself further.” (Thomson also made a strange discovery: nearly every landscape shown is the same valley. “The sensation of journey is an artful trick,” he wrote. “In reality, the cows must have trampled that one valley flat for a fortnight as the camera covered them from a compass of angles.”)

These days, Thomson’s preferred approach is to forget a film to the “point where déjà vu jostles the thing half recalled.” He told me that Ingmar Bergman, Luis Buñuel, and Max Ophuls are “directors who respond to this very well.” The act of re-watching can enable a deeper engagement with a particular film’s intentions and achievements. It is also likely to provoke thinking that is altogether more abstract, about movies and what happens when we watch them. Thomson says that the more times he sees a film, the more the experience makes him think about time—how moving images fudge time and freeze it, and how we mark it in our relationship with movies.

That’s another reason why “Muriel” doesn’t change very much on successive viewings: time couldn’t become Resnais’s subject any more clearly. Characters talk about people and events being late, timely, and old. Boulogne is described a “dump that feeds on memories.” A man yells at Bernard, “What time is it?” The “past” is invoked again and again. Hélène’s flat is full of antique clocks, and you can hear the tolling from a nearby tower. Even the film’s pace—frenetic yet glacial—makes you acutely aware of temporal paradoxes. Due to this pincer movement of theme and form, the sensations usually inspired by rewatching (nostalgia, boredom, estrangement, disappointment, déjà vu) are compressed into a single viewing.

Still, there’s fresh evidence of the film’s improbable more-ishness, its appeal to viewers who derived neither enjoyment nor understanding the first time around: a comment on the Rotten Tomatoes Web page for the film doubles as an ideal expression of the rewatcher’s open mind: “Oh God how I HATE HATE HATED this film in college. One of the most miserable film viewing experiences of my life. I suppose I should revisit it.”