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Creator-Preferred Adaptation: Not exactly, but this is probably one of the most amicable examples of a Hollywood remake of a foreign film in living memory. Alejandro Amenábar was delighted when he discovered that Cruise and Crowe wanted to remake Abre Los Ojos, and has stated that he considers the remake a worthy successor to the source film, comparing the two films to two brothers who have similar attitudes but different tastes. Crowe, for his part, directed the film in large part because he liked the original so much, and stated that he wants people to see both versions of the film.
Romance on the Set: Tom Cruise and Penelope Cruz started dating after working together in this movie. Although it is said that one of the main reasons why Cruise wanted to make the remake in the first place (apart from because he really liked the original Spanish movie) it's because he got infatuated with Cruz after watching Open Your Eyes.
Throw It In: The line "I'll tell you in another life, when we are both cats" was something Penelope Cruz said to Cameron Crowe in a moment of frustration. He loved it so much he made it a key part of the movie.