Sexuality
The film is about the budding of a young person's sexuality, not only his desire for sex and his attraction to other people, but also his emergent identity as a homosexual. The lush backdrop of northern Italy in the summer is a prime setting for Elio's sexual awakening, his libidinous eagerness to greet the world and learn more about it. After he falls in love with Oliver, he can barely contain his urges, masturbating with a peach, putting Oliver's bathing suit over his head to get closer to him, and seducing the older man clumsily and confidently. The film explores the story of a young person discovering their erotic impulses and embracing their sexuality, with all the embarrassment, excitement, and heartbreak that entails.
Secrets
A major component of Elio and Oliver's affair is the fact that it is a secret. They share hidden moments, always secreted away from others, and each of them carries on affairs with women in public. This alludes to the fact that they are pursuing a gay relationship in a time when such a connection was less widely accepted in society. Additionally, the secrecy of their love heightens its thrill and brings them even closer together. There is a kind of erotic excitement that each of them gets from being private about their connection to one another, and they barely speak to one another except to debate or seduce. A great deal of their love is wordless, inarticulate, and visceral.
Familial Closeness
While it may seem that Elio and Oliver's affair is secret and completely unseen by the surrounding world, Elio's parents seem to have an idea of what is going on, and they share knowing glances throughout about the little crush that their son has developed on the hunky academic staying with them. They are not the imagined middle-class parents of a gay child in the AIDS-era US. Rather, they share an almost ahistorical approval of their son's sexual awakening, and they encourage his exploration warmly. Intellectual and enlightened, they see their son's maturation as a natural and beautiful thing. Towards the end, Elio's father gives him an impassioned speech about the importance and dignity of his feelings for Oliver, urging him not to repress his heartache, but to embrace it.
Growth and Development
The film is about romantic awakening, but it is also about awakenings more generally, growing up and learning about the world. Even though he is intellectual and precocious, Elio is a naive and impressionable young man who has yet to experience his first sexual experience, his first love, his first heartbreak. The film follows him as he changes into a young man. This is highlighted by the note of Oliver's that he finds in the Heraclitus book: "The meaning of the river flowing is not that all things are changing so that we cannot encounter them twice, but that some things stay the same only by changing." In this, we see that a major theme is growth and change, the fact that only through growing can human beings connect with that which is unchangeable about themselves.
Heartache & Heartbreak
Throughout much of the film, we see Elio pained by his experience of desire, wishing so badly for Oliver to notice and acknowledge him, but not knowing how to express his feelings. We watch as he experiences the lilts and troughs of young love, worrying, waiting, consummating, wondering. We see his experience of heartache, his longing for a man that is so close to him, but who is, in many ways, so incomprehensible. Then, at the end, Oliver calls and tells him that he is marrying a woman, and that he will live his life as a straight man. This news shatters Elio, who is still in love with Oliver, and we watch him as he sits in front of the fireplace and weeps. The audience gets a front-row seat to Elio's feeling of heartbreak, a painful and shattering rite of passage.
Friendship
Elio is confused about his sexuality for much of the film, and often carries on an elaborate and performative affair with his girlfriend, Marzia, in order to make Oliver jealous. This is clearly painful for Marzia, who harbors real feelings for Elio, but he is unable to explain what is going on in his life. At the end, after he has returned from his trip to Rome with Oliver, Marzia finds him in a town square and tells him that she has no hard feelings towards him. In this way, Marzia lets him know that she has forgiven him for using her and that she wants to be friends, and the two of them make a vow to remain connected. Thus, in the wake of Oliver's departure, Elio finds that he has the comfort of friendship.
Antiquity
Elio's father is a professor of archaeology and studies the ancients, which is the area of study that has drawn Oliver there to stay with the Perlmans. Throughout, we hear quotes from philosophers of antiquity and see images of ancient statues, which often have some kind of homoerotic context. Antiquity is a lens through which the viewer is meant to perceive and think about Elio and Oliver's affair, as an extension of an ancient tradition of homoerotic affection and admiration.
