Martin Scorsese's portrayal of Jake LaMotta is probably the single greatest exploration of duality put to film. The film ruminates on a myriad of themes: fate vs choice, hero vs celebrity, fantasy vs reality, virgin/whore, strength vs weakness, masculinity vs femininity, dark vs light, and the most obvious control vs helplessness. These themes all cohere seamlessly in LaMotta, who is played to perfection by Robert DeNiro in the most striking example of method acting I've ever seen. LaMotta is a man obsessed with control, and it incites reactions of him as pathetically amusing to just plain pathetic; this is one of the hardest to watch central characters to watch you'll see. He simultaneously acts as protagonist and antagonist yet remains consistently unlikeable.
Nearly all of the directorial decisions (like the violence breaking up the slow pacing, and the film's being shot in B&W) are deliberate, adding immensely to its theme of duality, and in general to its intensity.
It's hard to believe this isn't even Scorsese's best film.