Marianne "Manina" Stuart (Joan Fontaine), a prominent concert pianist, meets David Lawrence (Joseph Cotten), a businessman, on a flight from Rome to New York. Their plane is diverted to Naples for engine repairs, and they decide to kill time by doing some sight-seeing.
At lunch, a recording of the Kurt Weill/Maxwell Anderson song "September Song", sung by Walter Huston, is playing. Manina is single, and David is unhappily married with a son in his late teens. They talk too long and miss their flight, and decide to stay on for a few days, getting to know each other. They quickly fall in love.
Then they hear that the plane they were scheduled to catch has crashed into the ocean, and all on board are presumed dead. Due to a clerical mixup, they were believed to have been among those aboard. A list of the victims is published in a newspaper they pick up. Thinking their absences won't make any difference to the larger world, they decide to "stay dead" and begin a new life together in Florence. They make no contact with their families or friends, including Lawrence's wife Catherine (Jessica Tandy) and son David Jr (Robert Arthur).
Manina had been originally intending to play Rachmaninoff's Piano Concerto No. 2 in New York, and she keeps up her practice during the secret affair. She also has contact with piano teacher Maria Salvatini (Françoise Rosay), who agrees not to reveal Manina is very much alive, but continues to tutor her.
David transfers a large sum of money to Maria Salvatini by issuing a check dated prior to the flight. They use the money as a nest egg for their life in Florence. Catherine and her son travel to Florence after hearing of this transfer to try to find out any more on David's fate from the woman he gave the money to. David Jr recognizes Manina's face from the list of presumed dead and puts two and two together that his father is alive. After this David's wife writes him a note and then leaves. Knowing their secret is out, Manina goes on to perform the Rachmaninoff concerto as originally planned in New York. In the end, Manina realizes she can't stay with David, that they tried to hide from the past but it caught up with them, and after her concert leaves, bidding David goodbye at the airport.
The primary music score was written by Victor Young.
"September Song", music by Kurt Weill, lyrics by Maxwell Anderson, is heard, originally in the recording by Walter Huston. Later, Johnny Wilson (Jimmy Lydon), a sailor, sings it live. Huston’s recording had been made in 1938, but the film gave it a new lease of life and it made it to the top of the 1950 hit parade.
The voice of Enrico Caruso is also heard in an off-screen recording.
The costume design was by Edith Head. The film was shot on location in Naples, Capri, Florence and other places in Italy.