In Mexico's Sonoran Desert, French scientist Claude Lacombe, and his American interpreter David Laughlin, along with other government scientific researchers, discover Flight 19, a squadron of World War II airplanes that disappeared more than 30 years earlier in the Bermuda Triangle. The planes are intact and operational, but there is no sign of the pilots. An old man who witnessed the event claimed that "the sun came out at night, and sang to him". Meanwhile, at an air traffic control center in Indianapolis, controllers listen as two commercial airline flights narrowly avoid a mid-air collision with an unidentified flying object (UFO). In Muncie, Indiana, 3-year-old Barry Guiler is awakened in the night when his toys start operating on their own. Fascinated, he gets out of bed and discovers someone or something (off-screen) in the kitchen. Playfully, he runs outside, forcing his mother, Jillian, to chase after him.
Investigating one of a series of large-scale power outages in Indiana, electrical maintenance worker Roy Neary experiences a close encounter with a huge UFO when it flies over his truck and lightly burns the side of his face with its bright lights. Chasing it, he almost hits Barry and Jillian, and they encounter more, smaller, UFOs, hovering low to the road surface, almost resembling cars. Neary follows police cars pursuing them, but the objects fly off into the night sky. Roy becomes fascinated by UFOs, much to the dismay of his wife, Ronnie. He also becomes increasingly obsessed with subliminal, mental images of a mountain-like shape and begins making models of it. Jillian also becomes obsessed with sketching a unique-looking mountain.
Lacombe, Laughlin, and various United Nations experts continue investigating increasing UFO activity and strange, related occurrences, such as finding the SS Cotopaxi – a ship that also disappeared in the Triangle 50 years earlier - inexplicably in the Gobi Desert. Witnesses in Dharamshala, India report the UFOs emit a particular sequence of five musical tones: D', E', C', C, G. Scientists broadcast the sequence to outer space and receive, in response, a seemingly meaningless string of six numbers repeated over and over (as short radio pulse sets). Using his background in cartography, Laughlin recognizes the numbers as a set of geographical coordinates pointing to Devils Tower, Wyoming. Lacombe and the U.S. military converge on Wyoming. The Army evacuates the entire area around Devils Tower by planting false reports in the media that a train wreck has spilled a toxic nerve gas, all the while preparing a secret landing zone for the UFOs and their occupants.
Meanwhile, Jillian is terrorized in her home by a UFO which descends from the clouds and causes appliances in her house to activate (including a telephone starting to play the five musical tones, faster and faster until the scene ends) as unseen beings try entering the house in every possible way, initially stopped by Jillian, until Barry, who joyfully seems to want to help the beings, is abducted by them. Shortly after, Roy's increasingly erratic behavior causes Ronnie to leave him with their three children. When a despairing Roy inadvertently sees a television news program about the train wreck near Devils Tower, he recognizes the mental image of a mountain. Jillian sees the same broadcast, and she and Roy, as well as others with similar visions and experiences, travel to the site in spite of the warnings about nerve gas.
While most of the civilians who are drawn to the site are apprehended by the Army, Roy and Jillian persist and make it to the secret landing zone just as dozens of UFOs appear in the night sky. Scientific specialists at the site begin to try to communicate with the UFOs by the use of light and sound from a large electrical billboard that is controlled by a synthesizer. After the UFOs leave, an enormous mothership lands at the site, also using light and sound to teach the specialists the aliens' basic tonal vocabulary. It then releases the missing pilots from Flight 19, as well as the missing sailors from the Cotopaxi and many other long-missing people, all from different past eras and all of whom have not aged since their abductions. Barry is also returned and reunited with a relieved Jillian.
As the aliens finally emerge from the mothership, the government officials decide to include Roy in a group of people whom they selected as potential travellers to join the mothership, and hastily prepare him. The aliens select Roy to join them on their travels, and after Roy enters the mothership, one of the aliens pauses for a few moments with the humans. Lacombe uses Curwen hand signs that correspond to the five-note alien tonal phrase. The alien replies with the same gestures, smiles, and returns to the ship which ascends into space.
