In October 2022, amid a flurry of media appearances promoting their film “Tàr,” the director Todd Field and the star Cate Blanchett made time to visit a cramped closet in Manhattan. This closet, which has become a sacred space for movie buffs, was once a disused bathroom at the headquarters of the Criterion Collection, a 40-year-old company dedicated to “gathering the greatest films from around the world” and making high-quality editions available to the public on DVD and Blu-ray and, more recently, through its streaming service, the Criterion Channel. Today Criterion uses the closet as its stockroom, housing films by some 600 directors from more than 50 countries — a catalog so synonymous with cinematic achievement that it has come to function as a kind of film Hall of Fame. Through a combination of luck, obsession and good taste, this 55-person company has become the arbiter of what makes a great movie, more so than any Hollywood studio or awards ceremony.