First major studio film of Writer/Director/Composer John Carpenter, who wrote the film's screenplay, which was originally titled "Eyes".
In both posters and newspaper ads, with taglines like "You can't always believe what you see..." Faye Dunaway's face appeared a little bit at a time, beginning just with the over-bright image of her eyes, and the rest of the facial features appearing in subsequent ads, until the face was featured completely in the final poster.
Tommy Lee Jones actually wrote his own monologue, unbeknownst to the Writers' Guild, but accredited it to the film's director, Irvin Kershner.
Faye Dunaway was dating ace British photographer Terry O'Neill at the time, who coached her for the role. (They later married, then divorced.)
Barbra Streisand, who was originally attached to star as Laura Mars, sings the theme song "Prisoner" from this movie. It's the only song that Streisand sings for a movie in which she does not appear. The fact that her then-partner, Jon Peters, produced the film might explain this.