Bryan Cranston's character, the unnamed host of a black-and-white television series, bears some resemblance to Rod Serling, host of the American sci-fi anthology, The Twilight Zone.
Once the alien descends into the desert, grabs a meteorite and flees, the stargazers are baffled by what they’ve seen but don’t attribute any malicious intent to the UFO.
Steven Spielberg features in the credits list of Asteroid City, a film that references his Close Encounters of The Third Kind, in which an alien landing becomes a mass attraction.
A roadrunner appears several times during the film, pausing only to produce a ‘beep-beep’ sound and then dash off, much like in the classic cartoon.
Jones Hall, (Jason Schwartzman) the actor playing Augie Steenbeck, pulls his sweater over his face in the acting studio, which seems to reference this photo of James Dean.