Call Me by Your Name follows the story of Elio, the 17-year-old sun of Jewish-American academics summering in Italy in the summer of 1983 over a period of six weeks. Every summer, his father works with and hosts an academic at their house. This year that academic is Oliver, a young American student, who is welcomed into their home with open arms.
From the start, Elio is drawn to Oliver, in spite of their differences. Elio is bookish and musical, often poring over a text or sitting at the piano. While Oliver is academic, he is more socially assured, and flirts with almost everyone. As the tension builds between them, through a series of intellectual discussions and day trips, they try to make the other jealous by having affairs with women.
As Oliver and Elio spend more time together, however, Elio ends up confessing his feelings of attraction. Oliver and Elio kiss, but things quickly change between them. Oliver grows distant and they stop conversing. Craving Oliver’s contact even more now, Elio sends him a letter. Oliver answers that they should meet at midnight, after a visit from a gay couple with whom Elio's parents are friends. That night, they end up having sex for the first time, and embark on an affair. They go to Rome together, but Oliver soon has to return to his life in America.
Elio returns to his home after Oliver has left, heartbroken. His father gives him a pep talk about the beauty of his relationship with Oliver, and encourages Elio not to repress his feelings.
A while later, Elio is in Italy for the winter holidays, and picks up a call from Oliver, who tells him he is engaged to a woman. Elio hangs up and cries.
