In what appears to be the Sonoran Desert; in or near Mexico, a cartographer named David Laughlin (Bob Balaban) is introduced to a French-speaking man named Claude Lacombe (renowned French director François Truffaut). Though David has been hired as Mr Lacombe's interpreter, he explains that he is actually a cartographer (a mapmaker).
The two men along with a crew soon find a strange sight: a circular ring of airplanes in brand-new condition, with fuel still in the tank. The planes are identified as belonging to 'Flight 19,' a group of Navel planes that were reported missing off the coast of Florida in the mid-40's. The men soon after find a local who reported the planes. David and Claude find the man has red sunburned marks on the side of his face. Through an interpreter, the sunburned man claims the sun came out that evening, and talked to him.
In an air traffic control tower in the US, some of the control tower receive reports of unidentified aircraft flying through the air and coming dangerously close to hitting an airplane. When the tower requests the planes in the vicinity of the incident if they wish to report a 'UFO (unidentified flying object),' both planes decide not to.
In Muncie, Indiana, a strange power outage blackens the area. This incident affects two different families of people.
The first is Jillian Guiler (Melinda Dillon). When she wakes in the middle of the night and finds her son Barry (Cary Guffey) missing, she wanders off into the countryside to find him.
The second person is Roy Neary (Richard Dreyfuss). Roy gets a call from the power company he works for, and goes out to answer a service call. However, stopping at a train's track, a number of metal objects in the vicinity (including Roy's truck) begin to act strangely. A strange craft appears overhead, and flashes bright lights at Roy before flying off. Once the craft has disappeared, Roy drives off, before almost hitting Barry on a hillside road.
As Jillian appears, several strangely-lit craft fly by, along with a bright red light at the tail end. Entranced by the strange objects, Roy gets back in his truck and gives chase, along with several local police cars. The strange objects fly off over the edge of a cliff, and as Roy and the officers watch, ascend into some thundering storm clouds overhead, as the darkened city underneath them regains power.
Roy returns to his family eager to tell of what he saw, but his wife Ronnie (Teri Garr) refuses to acknowledge her husband's flights of fancy. Even though Roy has red sunburns from being flashed by the craft he saw, she still doesn't 'believe.'
Some time afterwards, Roy meets up with Jillian and Barry, and Jillian relates how there seems to be a melody and an image of a mountain she cannot get out of her mind. Roy soon finds himself obsessing over the same mountain image, carving it in mashed potatoes as well as sculpting it out of putty or shaving cream.
Meanwhile, Bob and Claude have gone around the world and observed other strange phenomenon:
-A group of people in India have been chanting a strange 5-note sequence that they claim came from above.
-A missing ship named the Coat Appoxi has appeared in another desert region.
-Information gleaned from the musical notation sequence and a message indicates that there appears to be plans for the extraterrestrial life to descend to Earth. The Military and NASA coordinate a plan to create a false scare in the landing region that a toxic spill will make the area dangerous.
Back in Muncie, Jillian is shocked one evening when the same lights as before descend towards her home, and soon after abduct her son Barry. Still in a state of shock, Jillian takes her story to the news outlets.
Shortly thereafter, a person from the US Government sits down for a town hall chat with several locals in attendance (including Roy and his family), denying that there are UFO's, or that the government is covering up any such things.
Roy is slowly losing his mind over the strange images in his head, and finally drives his wife Ronnie to take their kids and leave. After they have left, Roy constructs an enormous miniature of a mountain in his family's living room, before seeing a news article on the television, showing Devil's Tower...the same structure he's been seeing in his mind!
Roy heads off towards Devil's Tower, only to encounter every one leaving in the wake of a (fake) chemical spill warning. Roy also finds Jillian there, and the two attempt to get to Devil's Tower, but are captured by some Military men.
Roy and Jillian are separated, with Roy brought before Bob and Claude. The two listen to Roy's story...a story that sounds similar to several other people who have been drawn to the mountainous structure nearby. The two make an impassioned plea to the Military Director at the base, but he refuses to believe their 'theory' that these people were 'invited,' and attempts to fly the civilians out of there.
Jillian and Roy manage to escape, making it to the other side of the mountain before night settles in, finding an enormous landing strip having been constructed. The two secretly make their way down as several little lit ships appear, before a giant 'mother ship' hovers down.
Using light and sound based on the 5-note motive, the aliens appear and release some humans who had been abducted previously (many having never aged). Barry is returned as well.
When Claude sees Roy has appeared as well, he and Roy decide that he (Roy) will go with several people meant to be swapped for the returnees by the aliens.
After Roy and several others board the ship, it takes off for distant space.