The protagonist, Marcello, is from a privileged background, portrayed through the decadence of his parents; his father in an asylum with syphilitic insanity, his mother using morphine, obtained from a lover, to blank the inexorable decay of her existence.
As a child, he was somewhere between seduced and raped by a stranger, a chauffeur. Marcello believes he killed the man after this incident.
He comes out as a man totally without faith or belief; in himself, in the catholic church and its god, in society. Marcello craves the mundane, as the title suggests he seeks to conform. He works through the Italian Fascist party, using contacts to get into the position of a political "policeman". He courts and marries Guilia, a pretty, gauche, naïve, submissive middle-class girl. He tells himself (and the priest) that he wants a normal unambitious life. However, he has no real belief in this as a real marriage, and even on his honeymoon is attracted to other women. The honeymoon takes them to Paris, where Marcello is to kill a Professor Quadri, who is an anti-Fascist activist and a former teacher of Marcello. There he meets Anna, she is everything Guilia is not, intelligent, ambitious, confident, revolutionary and genuinely edgy (including being bisexual) to Guilia's false audaciousness, honest to Guilia's middle-class politeness.
There first confrontation between Marcello and Quadri comes in Quadri's study, in an absolutely beautifully shot scene. Marcello closes one set of shutters as he enters, the light from the other open shutter fills half the shot where Quadri is standing. They discuss Marcello's thesis that he was working on before Quadri left Italy, it was an examination of Plato's allegory of the cave (I'm surprised more film directors don't mention it). After Quadri left, Marcello discarded that thesis and started another.
Between his attraction to Anna, and the persuasion of Quadri; once again Marcello display a lack of belief, this time in the Fascist state that employs him. He's trapped though, since also in Paris is an experienced Fascist "policeman", Manganiello, there to monitor Marcello and keep him to his mission.
Having explained the first ¾ of the film, I'll spare you a full explanation of the ending.
I was drawn to comparisons with Camus' Meursault. However, there is a fundamental distinction. Meursault accepts the inevitability of fate; Marcello despite no belief in anything constantly shifts and conforms to the strongest influence near him. With no true beliefs or loyalties he constantly betrays others and himself.
The photography is beautiful, with striking use of light and colour. The plot is psychologically complex, the characters are well constructed and well observed by the actors. Overall, an excellent film.