Roy Neary (Richard Dreyfuss) is an electrical lineman who, while sent out on emergency repairs, witnesses an unidentified flying object. Neary's wife (Teri Garr) and children are at first skeptical, then concerned, and eventually fearful, as Roy refuses to accept a "logical" explanation for what he saw and is prepared to give up his job, his home, and his family to pursue the "truth" about UFOs. Neary's obsession eventually puts him in contact with others who've had close encounters with alien spacecraft, including Jillian (Melinda Dillon), a single mother whose son disappeared during her UFO experience, and Claude Lacombe (François Truffaut), a French researcher who believes he can use a musical language to communicate with the alien visitors. Lacombe's theory is put to the test when a band of government researchers and underground UFO enthusiasts (including Neary) join for an exchange with alien visitors near Devil's Tower, Wyoming.