In August 1904, Sabina Spielrein arrives at the Burghölzli, the pre-eminent psychiatric hospital in Zürich, suffering from hysteria and begins a new course of treatment with the young Swiss doctor Carl Jung. He uses word association and dream interpretation as part of his approach to psychoanalysis and finds that Spielrein's condition was triggered by the humiliation and sexual arousal she felt as a child when her father spanked her naked. Jung and chief of medicine Eugen Bleuler recognize Spielrein's intelligence and energy and allow her to assist them in their experiments. She measures the physical reactions of subjects during word association, to provide empirical data as a scientific basis for psychoanalysis. She soon learns that much of this new science is founded on the doctors' observations of themselves, each other, and their families, not just their patients. The doctors, Jung and Freud, correspond at length before they meet, and begin sharing their dreams and analysing each other, and Freud himself soon adopts Jung as his heir and agent. Jung finds in Spielrein a kindred spirit, and their attraction deepens due to transference. Jung resists the idea of cheating on his wife, Emma, and breaking the taboo of sex with a patient, but his resolve is weakened by the wild and unrepentant confidences of his new patient Otto Gross, a brilliant, philandering, unstable psychoanalyst. Gross decries monogamy in general and suggests that resistance to transference is symptomatic of the repression of normal, healthy sexual impulses, exhorting Jung to indulge himself with abandon. Jung finally begins an affair with Spielrein, including rudimentary bondage and spanking. Things become even more tangled as he becomes her advisor to her dissertation; he publishes not only his studies of her as a patient but eventually her treatise as well. Spielrein wants to conceive a child with Jung, but he refuses. After he attempts to confine their relationship again to doctor and patient, she appeals to Freud for his professional help, and forces Jung to tell Freud the truth about their relationship, reminding him that she could have publicly damaged him but did not want to. Jung and Freud travel to America. However, cracks appear in their friendship as they begin to disagree more frequently on matters of psychoanalysis. Jung and Spielrein meet to work on her dissertation in Switzerland and begin their sexual relationship once more. However, after Jung refuses to leave his wife for her, Spielrein decides to go to Vienna. She meets Freud and says that although she sides with him, she believes he and Jung need to reconcile for psychoanalysis to continue to develop. Following Freud's collapse at an academic conference, he and Jung continue correspondence via letters. They decide to end their relationship after increasing hostilities and accusations regarding the differences in their conceptualisation of psychoanalysis. Spielrein marries a Russian doctor and, while pregnant, visits Jung and his wife. They discuss psychoanalysis and Jung's new mistress. Jung confides that his love for Spielrein made him a better person. The film's footnote reveals the eventual fates of the four analysts. Gross starved to death in Berlin in 1920. Freud died of cancer in London in 1939 after being driven out of Vienna by the Nazis. Spielrein trained several analysts in the Soviet Union before she and her two daughters were shot by the Nazis in 1942. Jung emerged from a nervous breakdown to become the world's leading psychologist before dying in 1961.

Okwe, a doctor in his home country (not initially named) who was forced to flee after being falsely accused of murdering his wife, lives in the United Kingdom as an undocumented immigrant. He drives a cab in London during the day and works at the front desk of a hotel at night, which is staffed by other immigrants, both documented and undocumented. He is pressed to treat other poor immigrants, including fellow cab drivers with venereal diseases, with scarce supplies provided by his friend Guo Yi, an employee at a hospital mortuary. Juliette, a sex worker who regularly conducts her business at the hotel, informs Okwe about a blocked toilet in one of the rooms, and he fishes out a human heart. The manager of the hotel, Juan, runs an illegal operation at the hotel wherein immigrants swap kidneys for forged passports. After learning of Okwe's past as a doctor, Juan pressures him to join his operation as a surgeon, but Okwe refuses. Senay is a Turkish Muslim seeking asylum who also works at the hotel as a cleaner. Her immigration status allows her to stay in the UK, provided she does not work; the hotel is a perfect cover because she is not named on its books. She allows Okwe to sleep on her sofa when she is not home, as she is from a conservative culture where men and women who are not married do not spend the night together under the same roof. After Senay is visited by Immigration Services, who inspect the hotel after finding a book of matches in her flat, Okwe prevents the officials from intercepting her. No longer able to work at the hotel, Senay begins working in a sweatshop making clothes, which is also raided by officials looking for undocumented immigrants, who the manager gets rid of. The manager allows Senay to keep her job and not report her to the authorities in return for her performing oral sex on him; she initially complies before proceeding to bite him. Okwe finds her a place to stay at the hospital mortuary, while Senay asks him to accept Juan's proposition in his organ business to raise money to travel to America. In desperation, Senay offers her kidney to Juan for a passport; Juan accepts the deal on condition he takes her virginity as well. Senay is later provided with a morning-after pill by Juliette. After learning of Senay's plan, Okwe agrees to perform the operation to ensure her safety, but only if Juan provides them both with passports under different names. After Juan delivers the passports, Okwe and Senay drug him, surgically remove his kidney, and sell it to Juan's contact. Okwe plans to use his new identity to return to his young daughter in Nigeria, and Senay plans to start a new life in New York. Before they part at Stansted Airport, they mouth the words "I love you" to each other, and she gives him her cousin's address in New York. Senay boards her plane, and Okwe calls his daughter long-distance to tell her he is finally coming home.

Two years after the Apollo 17 mission, the crew of the cancelled Apollo 18 mission consisting of Commander Nathan Walker, Lieutenant Colonel John Grey, and Captain Ben Anderson are informed that it will proceed as a top-secret Department of Defense (DoD) mission to place an early warning detector on the Moon for ICBM attacks from the USSR. Grey remains aboard Apollo command module Freedom while Walker and Anderson land in Apollo Lunar Module Liberty to plant the detector. Anderson takes back rock samples and the two return to Liberty. The samples cause small disturbances, which Houston attributes to interference from the detector. The next day, Anderson discovers footprints that lead them to an abandoned but functioning Soviet LK lander. They discover a crater with a dead cosmonaut, to which Houston dismisses Walker's queries. While sleeping, Walker is awakened by strange noises and an object bumping into the lander. Walker and Anderson complete the mission and prepare to leave, but the launch is aborted when Liberty suffers violent shaking, which they discover is a result of damaged foil. Nearby, they find non-human tracks outside the Liberty alongside damaged equipment. Walker is horrified at a spider-like creature that has entered his spacesuit and disappears before Anderson finds him unconscious near Liberty, which Walker later denies happening. Later, Anderson removes a Moon rock embedded in Walker. Walker smashes the rock, contaminating the ship. Due to interference from an unknown source, the two are unable to contact Houston or Grey. Anderson speculates that the device is meant to monitor the aliens and that it is the source of the interference. They attempt to deactivate the device but find it destroyed. Walker begins to become contentious and paranoid, and they discover that the aliens are camouflaged as Moon rocks. In an attempt to destroy the cameras inside Liberty, Walker destroys other controls, causing the ship to depressurize. While traveling to the Soviet LK lander to get oxygen, Walker intentionally crashes the rover, believing that he will spread the infection on Earth if he were to return. Anderson awakens and finds Walker getting pulled into a crater by the aliens. Anderson fails to rescue him and flees to the Soviet LK. He uses the radio to contact the USSR Mission Control, who connect him to the DoD. The Deputy Secretary informs Anderson that they cannot allow him to return to Earth, admitting that they are aware of the situation and incorrectly believe that he is also infected. Grey contacts Anderson, and they plan to return him to Freedom. As Anderson prepares to launch, Walker suddenly appears and demands to be let in before being suddenly swarmed by the aliens, who kill him. Anderson launches, but the DoD informs Grey that he is to abort the rescue, or they will not allow him to return either. The LK enters orbit and, while in free fall, the aliens attack and infect Anderson. Anderson is unable to control the ship, and he collides with Freedom. The U.S. government states that the astronauts were killed in various jet accidents that left their bodies unrecoverable. They note that many of the rock samples returned from previous Apollo missions given to dignitaries are now missing.

Phil's wife Kim, the den mother of the local Cub Scout pack, gives a pinewood derby kit to each of the Cub Scouts. Although the boys are supposed to make their own cars from the kits, with appropriate adult supervision, the four dads obsessively take over the project, totally excluding the boys. As each man becomes more and more obsessed with building the fastest car, their wives eventually become so annoyed that they leave the house, taking their sons with them. Soon, "Big Jimmy" is the first to break secrecy to talk to Blaine, and the two of them then talk to Phil, showing him on the title page of the Pinewood Derby Bible that Ace Montana is the author. Not only that, but the car Ace built as an eight-year-old boy in California still holds the record for the fastest pinewood derby car on record. The three men decide to collaborate to build one car that will beat. To this end, they steal Ace's record holding car to reverse-engineer it, finding out that Ace's real name is Stacy Lynn, but are nearly caught in the act of returning it. The three men then succeed in building a fast car that will break the record, and Blaine and Jimmy decide that Phil should have the honor of having his son enter the car in the competition. At the Derby, the men and their wives are re-united. Kim tells Phil that their son Brady (Adam Hicks) has built his own car while staying with his grandfather, with advice from grandpa's neighbor, and she challenges him to "do the right thing". After some soul-searching, Phil passes up the car the three men built and allows Brady to register his car for the race – but "Big Jimmy" still wants to beat Ace, and takes the car for his son to enter. After several races, the competition comes down to six finalists, including Ace's, Brady's, and the car the three men built. In the final race their car is leading the pack but loses a wheel. Ace's car then takes the lead, but on the flat part of the track, Brady's car takes the lead and finishes first, setting a new pinewood derby record. Ace is shocked but makes a gesture of congratulating the Davises; still, the minute he leaves the room, he throws a temper tantrum. When Phil asks Brady who grandpa's neighbor was who gave him advice, Brady points out a man in the audience, who turns out to be the man in the instructional video Phil has been watching to help design his car.