Media mogul Bill Parrish is contemplating a merger with another media giant. Meanwhile, his eldest daughter, Alison, is planning an elaborate 65th birthday party for him. His younger daughter Susan, a resident in internal medicine, has a relationship with Drew, one of Bill's board members.

Businessman Adrián Doria is out on bail after being arrested for the murder of his lover, Laura Vidal. His lawyer, Félix Leiva, hires attorney Virginia Goodman, who visits him at his apartment with the news that the prosecutor has found a witness who will be testifying in front of a judge soon; they have three hours to come up with a defense, so Virginia urges Adrián to tell her the whole truth.

A stranger using the alias "Fermat" invites several people to attend a convention of the country's best mathematicians. To accept the invitation, each must solve a math puzzle. Upon receipt of the correct solution, each receives as an alias the name of a famous mathematician or philosopher; they are forbidden to reveal their true identities. Each is instructed to arrive at a specific place and time, alone and without a cell phone, to work on "the greatest enigma".

In 1965, sixteen-year-old Sylvia Likens and her disabled fifteen-year-old sister, Jenny, are left in the care of an impoverished woman named Gertrude Baniszewski, a church acquaintance and mother to Paula, Johnny, Stephanie, and several younger children. Sylvia and Jenny's parents, Lester and Betty, work in the carnival circuit and leave on a tour. Gertrude agrees to take care of Sylvia and Jenny for a fee of $20 per week.

A mother and daughter drive along a deserted country road at night while having an argument and crash their vehicle. The mother goes out of the car to check the engine but disappears. The daughter calls out for her but her call is repeated from the woods by a soft whispering voice. The daughter attempts to call the police but is strangled to death.

At a remote Hungarian military outpost, orderly Morosgoványi Vendel lives a wretched existence of servitude beneath the heel of his lieutenant, Öreg Balatony Kálmán. Condemned to performing menial duties for the officer and his family while sleeping in an unheated shack next to the latrines, Morosgoványi frequently escapes into fantasy. So realistic are these fantasies that in one ambiguous instance, Morosgoványi sleeps with and impregnates the lieutenant's wife and "wakes up" to find himself engaged in an act of sodomy with a slaughtered pig. Upon seeing this, the lieutenant promptly executes Morosgoványi and raises the son, Balatony Kálmán, as his own.

A meteorite brings a malevolent, sentient extraterrestrial parasite to Earth. The parasite enters the town of Wheelsy, South Carolina, where it infects wealthy resident Grant Grant by taking over his body and absorbing his mind. With the alien in control of him, Grant begins to transform into a grotesque, tentacled monstrosity. He also abducts and infects a local woman, Brenda, to serve as a breeder for his alien larvae. His wife Starla becomes suspicious over the changes in his appearance and behavior, leading to Grant attacking her. When the police arrive to rescue Starla, Grant flees.

In Berlin, the pederast serial killer Gabriel Engel, who later admitted to brutally killing 13 boys and painted impressive religious works of art with their blood, is accidentally taken during an overnight operation. Commissioner Seiler is charged with the interrogation of the murderer.

A gothic high-school comedy with a Carrie-like story. A bickering teen couple, Wally (Michael Showalter) and Buttercup (Hayley DuMond) visit Jojo (Keith Carradine)’s Diner for a drink. Since they have relationship issues with each other, Jojo decides to tell a story about a couple like them. The story he quotes is “a tale of the prom, of love, of Cherri and Spud.”

Timoteo, a surgeon, gets the shocking news that his fifteen-year-old daughter Angela has been seriously injured in a motorcycle accident. As she is operated upon, Timoteo looks out of a window to see (or imagines seeing) a woman, her back facing him, proceeding to sit down on a chair in the rain outside. He notices her prominent red heels and turns away in disbelief, indicating he was familiar with them. His subsequent reminiscences about an old affair comprise the remainder of the film.