The story is about a soldier who has participated in the war of Vietnam and is now back lonely and gripped by death. He becomes very miserable, and then a woman enters his life to heal him. He then directs all his energy in assassinating the bad guys.
De Niro ... manages to be as sad as he is frightening. From his general discomfort with others and his feeble attempts at communication, it's possible to recognize the root cause of Travis' inner distress as a terrible longing for approval.
[Scorsese] seems to need scripts with well-designed humor and performers with the spirit of Ellen Burstyn to compensate for what seems to be a fundamentally depressed view of life and the belief that sobriety is the equivalent of seriousness.
As with John Wayne's Ethan Edwards (Travis's spiritual forefather), his thwarted patriarchal possessiveness is not tempered by anything like genuine concern, yet it is enough... to make him a peculiarly American folk hero.