It is not a pedophile movie, don't be ridiculous, but it is not a masterpiece.

Rating: 4/10 (26 December 2017)

I have watched this film on two different levels. First is like a sugary-water romantic coming of age film and second is like a youth-fetishistic film. I have enjoyed the first level, although it is a bit to long with many unnecessary scenes. I don't see the reason of mentioning the partizans and second WW, and lots of the scenes seem too staged. From the discussion about old german tale to the father's speech near the end. But, still if you watch this film like a light romantic movie seen through the eyes of Elio you will be OK.
But, if you want to dig deeper, you are entering some murky waters.
Oliver is not very clear character. We don't know from the beginning if he is gay, bi or straight. We assume he is straight, he is going out with the girl and doesn't show any interest for Elio. Because of that it can be interpreted that his sexual feelings are awakened intellectually, through the archaeological findings and slides of Greek sculptures of ambiguous young boys and the speech about them which Elio's father is telling to Oliver like some kind of incite for Oliver to go after Elio. This interpretation would be more interesting to me than later revelation that he was attracted to Elio from the start. Oliver is then just a character who is attracted to younger boys. I don't mean pedophile! He doesn't discover his homosexuality in the proces of friendship with Elio, but he is determined from the start. He is the type of men who are attracted only to the youth. He is not interested in men, just young boys. Later, after summer is finished he goes back to his heteronormative life with the future wife to be. For him Elio is just a summer escapade, although he behaved very well and wise towards Elio. He is not a bad guy.
But author's films are not abut the characters anyway, they are about authors themselves. They choose themes which are closer to them and this movie is therefore a proclamation of fetichism towards youth. Nothing wrong with that. That is a legitimate theme. Only I didn't liked the manipulation and bypassing of it, camouflaging it with the coming of age theme. Father's monolog to Elio near the end confirms that youth fethisism assumption.
"When you get older no one will look at you, let a lone touch you" said father to Elio, and he also confess that he had romance with the man in his youth. Unfulfilled and therefore cemented like a fetish towards youth in his older days. This is why he envies Elio and why he is so encouraging for their affair. Not because his libertarian, educated and therefore open minded stance.
"Does mother knows?" asks Elio. "No" replies father. We are not sure if he asks about his own affair with the Oliver or father affair in the past, but judging from the mother's behaviour through the whole movie it can be assumed that this question refers to the father's past. He is not open towards his own openminded wife. He keeps his youth affair like a secret. Allowing therefore this secret to develop in to a fetish.
And to conclude, I didn't like the end scene, that forced tear jerker. It is like they wanted us to feel something in this too pretentious and too staged movie. Off course you will cry if you see someone crying and suffering for 5 minutes if you have any empathy in yourself. Manipulations like that, plus too much unnecessary parts in the movie are not features of good directors. Maybe in the future Luca Guadagnino will develop his crafts better but till then I will give this film 4 stars.