DeNiro tried to get Scorsese to make this movie for years but Scorsese resisted. He couldn't find an interesting, unique way into the story and didn't want to do just another boxer-with-a-tough life movie. He was also going through the late stages of cocaine addiction and felt that he had nothing left to offer the world of movie-making. DeNiro was persistent though and eventually Scorsese caved in, cleaned himself up and agreed to take it on.
Scorsese wanted a different look for this film, one of the reasons he decided to shoot in black and white. He reportedly was also bothered (from a strictly professional point of view) by the way that color film faded over time and didn't want this film to suffer that fate. He was also particular about how the fight sequences were shot; changing the size of the ring being used in order to elicit different emotional responses, putting a cameraman in the ring with the actors in order to capture the emotions of the fighters and delicately choreographing the fight sequences for maximum dramatic effect.
Production actually shut down for a time during the shoot so that DeNiro could go on an eating binge to prepare for the later scenes depicting the post retirement LaMotta. DeNiro returned from his binge some 50% heavier than he was during the first part of the shoot and suffered from back and breathing problems.
The finished product is one of stark beauty and gruesome confession. Both the filmmaker and his star push the envelope to the breaking point without apology. They had to. Any other treatment of such a blood-stained life would have been disingenuous. For their troubles the film was nominated for 8 academy awards and won 2, including best actor for Robert DeNiro. Though some critics of the day took issue with the hyper-realistic depiction of violence the film has since been recognized almost universally as one of the greatest American films of all time (and is number 3 on my list of top 10 films of the 80s).
Raging Bull -1980 - Trailer