The story is familiar to everyone (it's been around since 1719)—of the British sailor who is stranded on an island after his ship is wrecked and must eke out an existence there without hope of rescue, despite his lack of experience taking care of himself. Also, there is the man "Friday," who eventually becomes his companion on the island, leading to the "noble savage" mythology that is trucked around whenever somebody wants to point to relative "worth's" of races within the humanoid one.
But, Buñuel, one of the peskiest of directors has nothing to do with all that, and the surrealist—and realist—in him, takes this Robinson Crusoe to some little-known parts of the island in this version of the adventure. For example, Robinson Crusoe is on that ship as part of his work as a slave-trader, its wrecking serving as some kind of retribution for its business, and his exile a learning experience for what it is like for a man to have no choices in the world.
Crusoe is able to swim back to the ship to get a good amount of supplies before it finally succumbs to the sea, and manages to rescue a cat, Sam, from the wreckage. Once back on his island, with a raft so piled with supplies that it must have been in constant danger of sinking, he finds the Captain's dog, Rex, has also survived and made it to land. With that troika of inhabitants comes the most interesting part of the film, where Crusoe explores the island, sets up fire-stations in case a ship should sail by, hunts game, starts to raise livestock from the wild goats that live on the island, builds a walled compound around a make-shift cave where he lives. When he runs out of bread from the ship, he starts to raise his own wheat and grain and makes his own. A rescued bible provides study, and he even takes up pottery. He has a lot of time and quite a bit of resources.
Years go by. Rex dies of natural causes, and Crusoe keeps to his daily routine, living well if eccentric in his ways, until one day he notices that his island has been invaded by cannibals. Being so industrious, you'd expect him to maybe start a small business, given the new source of traffic, but, instead he manages to rescue one of the intended victims and names him "Friday"* (Jaime Fernández) after the day of the week on which they met (Crusoe has an elaborate calendar).
Not sure of Friday's eating habits, Crusoe returns to his old ways and puts the native under metal restraints that he carried over with him from the slave ship. Before long, he learns to trust the man, and one begins to wonder what the hierarchy between them is. The native is "Friday." Crusoe is, disquietingly, "Master." When Friday is barbering Crusoe's hair and the voice-over says it was a sublime time on the island, one is about to protest, when he gets up, the two exchange places and the former slaver cuts Friday's hair in reciprocity. Buñuel, you crafty old Marxist. "We found that two working together could do much more than working separately." We won't spoil the part where Crusoe and Friday debate the Bible.
And as far as surrealism, the closest Buñuel comes to it is in a Crusoe fever-dream, where he is warned by his father (also played by O'Herlihy) never to stray from his native land (Buñuel, a Spaniard was living in Mexico City at the time, after spending a few years in the United States) with the sequence intercut with shots of the father (or is it an elderly Crusoe) drowning.
O'Herlihy is mostly known for his later career of playing ancient, menacing autocrats, but here he is a revelation, and it is, frankly, amazing that the film had enough attention that he was nominated for a Best Actor Oscar, the same year as Bogart for The Caine Mutiny, Bing Crosby for The Country Girl (an amazing performance, that), James Mason in A Star is Born, and the winner, Marlon Brando for On the Waterfront. Tough year.
It's interesting to note that Robinson Crusoe on Mars has a release in the Criterion Collection (not to quibble, I regard RCOM fondly), but this adult-oriented family film by one of the great directors of the 20th century is not.
*But, not T.G.I. Friday, because that would be something of a sick joke that nobody'd get until they invented shopping malls.