Call Me By Your Name details the love story of Elio and Oliver, two young men who spend a summer together on the Italian Riviera and develop a bond that shapes their view of love for the rest of their lives. Elio is a precocious 17-year-old who spends summers with his family in their villa on the Italian Riviera. Oliver is a brilliant and handsome 24-year-old post-doctoral scholar from America who spends a summer in the mid-1980s at Elio's villa. Elio's parents select Oliver to live with them for six weeks as part of an annual fellowship that they offer to young scholars, with the purpose of helping them revise a manuscript for publication and aiding Elio's father—who is himself an academic—with his paperwork. Call Me By Your Name is a story about obsessive love, the passage of time, and life-defining memories.
The novel is told through Elio's first-person narration, recounting his memories of Oliver and their subsequent relationship. The novel begins with his first memories of Oliver: Oliver's typical farewell, "Later!", which Elio finds strange, cold, and indifferent. In his first few weeks at the villa, Oliver charms and befriends the residents and neighbors of the villa. Elio, who is introverted and shy, reflects on the beginning of his infatuation with Oliver, analyzing all of Oliver's words and mannerisms as he secretly pines for a more intimate relationship with Oliver. The desire that Elio feels for Oliver is at once overwhelming and sublime, a feeling stronger than any he has felt before, but he finds himself unable to express his feelings or talk about them with anyone, for fear of shame and rejection. Oliver's apparent coldness and indifference pain Elio, who labors to conceal his feelings from Oliver with affected silence and indifference on his part.
Elio and Oliver find common interests in literature, music, philosophy, and exercise; a friendship blooms between them. Elio admires Oliver's confidence and self-possessed attitude, taking note of how "okay" he seems with many things in his life, including criticism, his vices, his relationships, and his identity as a Jewish man. The latter makes a strong impression on Elio, whose family is also Jewish but who makes a point of keeping quiet about it in a majority Catholic country. Oliver's confidence on this matter emboldens Elio and makes him feel that Oliver could be his soulmate.
In the days leading up to Elio's confession of his attraction, Oliver begins seeing a neighbor of Elio's named Chiara. The two share a number of 'citte': dates, crushes, and mini-infatuations. Elio reflects on his attraction to both Oliver and Chiara and looks for signs that their relationship is sexual, both to his excitement and frustration. When he attempts to talk to Oliver about Chiara, seemingly in favor of their relationship and trying to set them up, Oliver shuts him down, declaring later that he is not interested in her. At the same time, Elio's parents beg him to spend more time with friends and enjoy his youth; trying to get his mind off of his desire for Oliver, he begins spending time with a girl his age, Marzia. Elio and Marzia's dates are sexual but not romantic, and Marzia keeps a wary emotional distance from Elio, seeing through his niceties to know that he is not actually interested in her.
On a trip to the nearby town of B., Elio alludes to his desire for Oliver, and Oliver tells him that they shouldn't talk about such things. Elio invites him to his secret solitary spot where he comes to read, the same berm where Monet used to paint. Oliver kisses Elio to appease his desire, but he wishes not to go any further for fear of doing anything that would make them feel ashamed. Elio has a hard time reading Oliver's intentions, but Oliver conceals his own desire for Elio out of shyness and fear of getting his own emotions entangled. The following weeks are witness to much silence and avoidance between the pair, until Elio decides to break their silence. Oliver invites him to his room at midnight and the two make love, after which Oliver holds Elio's gaze and asks him to call him by his name. After their night together, Elio feels confusion and frustration, unsure where his relationship with Oliver stands or where it is going, but Oliver warms up to him and a romance blossoms.
As Oliver's fellowship comes to an end, he and Elio take a trip to Rome where Oliver will spend his last three days in Italy. There, they spend a romantic vacation, spending one night with a group of revelers at a book-release party. The celebrated poet makes a speech about the nature of desire as a universal human experience. Elio becomes too intoxicated and vomits in a square; Oliver helps him recuperate, and they sing Neapolitan songs with strangers on a street. Elio's memory of kissing Oliver on the square becomes his favorite memory of Oliver for the rest of his life.
Oliver returns to the United States and Elio returns to his villa. Before departing, Oliver leaves Elio his billowy blue shirt as a memento. They promise to stay in contact; over the phone, Oliver tells Elio that he, too, took a memento from his room: a postcard depicting Monet's berm. Elio's father reveals to him that he knew about the affair and that he approves. He tells Elio that what he had with Oliver was a special, rare occurrence, something he himself never found in his life. The next year, Oliver marries a woman and goes on to father two children. In the years that follow, Elio continues to reflect on his experience with Oliver and sees it as a fulcrum around which the other romantic experiences in his life revolve. In vague terms, he mentions that he had many relationships after Oliver, but none as memorable and life-defining as Oliver. Elio and Oliver cross paths again at a New England college where Oliver teaches, his boys now teenagers; they share drinks and reminisce.
Years after that—twenty years after the events of his summer with Elio, and after the death of Elio's father—Oliver has an overnight stay at the villa en route to another Italian city. Elio walks Oliver through the villa and they reminisce about his father. Oliver tells Elio that he is just like him—that he "remembers everything." Elio concludes the novel by wishing to tell Oliver that when he boards his taxi the following morning, if he truly is like him, he should hold his gaze and call him by his name just as he did on their first night together.