Kanopy’s offerings vary depending on where you live. Some collections and some titles may not be available at all; some may be available to an education-affiliated account but not to a public library-affiliated account. The New York Public Library version of the service offers 420 movies from the Criterion Collection’s deep library of international classics (from directors including Ingmar Bergman, Orson Welles and Charlie Chaplin) and contemporary art house films.

Kanopy works like a standard paid streaming service, with limitations. Just as when you take a book out from the library and have a circumscribed amount of time to keep it, so it is with the movies here. Once you press “play” on a given movie, you have three days to watch it, as many times as you like, which uses up one play credit. The number of play credits for each user is determined by the library to which the membership is attached, not by the service. The New York Public Library offers Kanopy users 10 play credits a month. (Members affiliated with educational institutions get unlimited plays.)

Scrolling down the home page of the app version is awe-inspiring. In horizontal rows, 18 categories are presented, beginning with Criterion films. The others include “Popular Documentaries,” “Independent Films,” “World Cinema,” “Staff Picks,” “Audience Picks,” “New York Times Critics’ Picks” and my favorite, “Films Starring Actors From ‘Game of Thrones.’” There’s a fair amount of cross-categorization — you have to scroll far into “Classic Cinema” before you find a non-Criterion title. I was struck, and not in a bad way, by the occasional randomness of the selection. The unsophisticated but often laugh-out-loud funny 1977 anthology comedy “Kentucky Fried Movie” is here. As is the underrated 2000 prison drama “Animal Factory,” directed by Steve Buscemi and starring Willem Dafoe. As is “Boondock Saints,” an elaborate 1999 boondoggle of a crime picture that has somehow managed to attract a cult, also starring Mr. Dafoe.

In a phone interview, I asked Olivia Humphrey, Kanopy’s founder and chief executive, about such results. Many of the titles on the site are added via a “search and find” feature. College professors who need particular movies to assign to their students request titles, and Kanopy looks for them and tries to secure licensing rights.

Licensing movies is a byzantine business. I know of an independent DVD label owner whose inquiries into various obscure and hard-to-find titles in studio vaults was met with the response that the films were of such low priority that it wasn’t even worth it to do the paperwork to create an agreement. Ms. Humphrey told me that Kanopy had about 40 percent success with its searches, which is impressive, all things considered. “And yes, the challenge is usually not in finding the movie but in acquiring the rights,” she said. (I inferred from our chat that the presence of the two wildly disparate Dafoe films might have been because of some American academic researching the actor’s work.)