In the midst of a swirling sandstorm, French scientist Claude Lacombe and his interpreter, David Laughlin, join other UFO researchers in making a shocking discovery. Abandoned in the Sonoran Desert of Mexico are the five planes from Flight 19, Navy bombers that went missing over the Bermuda Triangle in 1945.
How they ended up in the desert, in mint condition with fuel in the tanks and family photos in the cockpits, is a bit of a puzzle.
Lacombe, Laughlin, and the team globetrot their way from one unexplained phenomenon to another. They locate the Cotopaxi, a ship that went missing in the Bermuda Triangle in 1925, in the landlocked Gobi Desert of Mongolia. In India, they investigate a group of men chanting a five-tone hymn they claim to have learned from the heavens. Back in America, a research team transmits the five-tonal phrase into space and receives a signal from an unknown entity, providing them coordinates that point to Wyoming.
While the research team is doing its thing, the UFOs visit Muncie, Indiana. Whatever their reasons for visiting Muncie—the cars or the cows or Ball State University's geothermal energy project—they wake up three-year-old Barry Guiler, who goes outside to follow the pretty lights and say hi to his new friends. His mother, Jillian, awakens to see her son wander into the woods, and goes running to retrieve him.
When the UFO presence messes with power grids across the county, electrician Roy Neary is sent to fix the problem and has a close encounter with a UFO on a back road. Roy becomes obsessed with his unexplainable experience while his wife, Ronnie, tries to convince him to forget it. He begins to see a mysterious shape half-formed in his mind. He desperately sculpts the shape from anything he can get his hands on—clay, shaving cream, mashed potatoes—but nothing looks right.
He's a total emotional wreck.
The UFOs revisit Barry and Jillian. They play a game of haunted house tag with Barry, much to Jillian's horror. She tries to get him, but Barry escapes through the doggy door and is abducted.
Back at the government's UFO research headquarters, the military's trying to figure out a way to keep the populace out of the vicinity of the Wyoming landing site the aliens have apparently proposed. They decide to spread information that there's a chemical spill that's emitting toxic gases that makes it necessary to evacuate people pronto.
Meanwhile, Roy continues to obsess over his close encounter.
He's getting more and more anguished about not being able to understand what's happening to him. His family is freaked out by his behavior. When Roy starts shoveling dirt and shrubs into the kitchen to build a giant sculpture, that's the last straw for Ronnie. She packs the children into the car and drives away.
Alone, Roy changes into an obsessed recluse, constructing a giant model of a laccolith in his living room. By a huge coincidence, Roy notices a news story about a chemical spill near Devil's Tower, Wyoming. Devil's Tower looks exactly like the mountainous image he's been preoccupied with.
Roy jumps in the car and heads for Wyoming; he sees Jillian there. They sneak into the evacuation zone with Roy believing, rightly so, that the chemical spill story is a government coverup. They're both captured, and Roy is interrogated by Lacombe and Laughlin. After the interrogation, Lacombe tries to convince Major Walsh that the people drawn to Devil's Tower should be allowed to stay. They've been "invited."
Roy and Jillian manage to escape and find their way to Devil's Tower. There, they find a landing site the government built for the alien arrival. Hidden in a rocky outcrop, they watch as the research team makes first contact, communicating with three UFOs using the five-tonal phrase and a rock concert's worth of gear.
After a conversation of light and sound, the mother ship lands and opens its bay doors. A host of abductees walk out of the ship, including the somewhat dazed Flight 19 pilots, a cheerleader, and a dog.
Jillian and Barry are reunited, while Lacombe locates Roy in the crowd to ask him what he wants. Roy responds that he just wants to know it's really happening. Lacombe pulls some strings and gets Roy a spot on Project Mayflower, a group of scientists and astronauts chosen to go with the aliens. As adorable aliens gently lead Roy aboard the mother ship, he turns to give Lacombe and Jillian a final smile goodbye.
One final alien emerges from the mother ship to meet Lacombe. Unable to talk to the creature, Lacombe teaches it the sign language for the five-tonal phrase. The alien repeats the motion, and they smile at each other. The mother ship leaves with Roy aboard and continues its journey through the universe…probably to pick up other intergalactic hitchhikers.