The method being referred to in A Dangerous Method (2011) is psychoanalysis, as pioneered by Sigmund Freud (1856-1939). The danger referred to is that of freeing people from their sexual repressions. The film revolves around the relationship between Freud and his younger colleague, Carl Jung (1875-1961), and the relationship between him and Sabina Spielrein, his former patient and eventual lover and colleague. She also had an affair with Freud, but it was not shown in the film. Keira Knightley plays the Russian woman a bit too strongly in the first few scenes. In terms of the acting, Knightley exaggerates facial contortions as if fishing for an Oscar out of sheer emotionality. In terms of the narrative, Spielrein’s “transformation,” or cure, is hard to take as credible because it is so drastic within a year or two. Before long, she is behaving completely normal and even attending medical school. The film’s merits lie not with the acting, but, rather, with the intellectual content, whose salience and integration into a good narrative is rare in Hollywood. It is due to this feature that the film is apt to stay with a viewer for some time.
The full essay is at "A Dangerous Method."