In 1951, mathematician Alan Turing is questioned by police after an apparent home break-in, and he obliquely refers to his work at Bletchley Park during World War II. In 1928, Turing, constantly bullied at boarding school, befriends Christopher Morcom, who sparks his interest in cryptography. Turing develops romantic feelings, but Christopher dies of bovine tuberculosis before he can confess. When Britain declares war on Germany in 1939, Turing is an established mathematician. He joins the cryptography team of Hugh Alexander, John Cairncross, Peter Hilton, Keith Furman, and Charles Richards in Bletchley Park, directed by Commander Alastair Denniston. Their main employment is analysis of the Enigma machine the Wehrmacht uses to send coded messages. Difficult to work with, and believing his colleagues to be inferior, Turing works alone to design a deciphering machine, which he names "Christopher". When Denniston refuses to fund the £100,000 construction cost, Turing contacts Prime Minister Winston Churchill who appoints him as team leader and provides the funds. Turing then fires Furman and Richards and places a difficult crossword in newspapers as a test to find replacements. Cambridge graduate Joan Clarke passes Turing's test but her family refuses her permission to work with the male cryptographers. Turing arranges for her to live and work with the women who intercept the messages, and shares his plans with her. Clarke helps Turing warm to the others, who begin to respect him. Turing's machine is constructed but cannot determine the Enigma encryption settings quickly enough, as the Germans reset them each day. Denniston orders it destroyed and Turing fired, and the other cryptographers threaten to leave. When Clarke plans to quit because of her parents, Turing proposes, which she accepts. During their engagement party, Turing confirms his homosexuality to Cairncross, who advises him to keep it a secret. Overhearing a clerk talking about messages received from the same German coder, Turing has an epiphany: he can program the machine to decode words he knows exist in certain messages. The theory is proven correct when the German coder consistently opens messages with a standard plaintext German script, which reveals enough of the daily Enigma code to permit decoding of that day's messages. The cryptographers celebrate this breakthrough. Discovering through decoded intercepts that a convoy is in danger of a German attack, Turing fears a sudden response will notify the Germans that Enigma is compromised and change it. The team concludes they cannot act on every decoded message, and they issue no warning about the attack on the convoy, even though Peter, whose brother is serving in the convoy, begs them. Turing creates a statistical model to select which intelligence to act on, to maximize effect on the enemy while minimizing the risk of German suspicion. Turing confronts Cairncross, who he has uncovered as a Soviet spy. Cairncross argues the Soviets are allies working for the same goals, and threatens to retaliate by disclosing Turing's sexuality. When MI6 agent Stewart Menzies appears to threaten Clarke, Turing shares his revelation about Cairncross. Menzies reveals in turn that he already knew, and is using Cairncross to leak misinformation to the Soviets for British benefit. Turing urges Clarke to leave Bletchley Park and admits his sexuality. She admits always being suspicious but insists they would have been happy together anyway. Fearing for her safety, Turing replies he never cared for her, and only used her for her cryptography skills. The heartbroken Clarke stays on, defying her parents and Turing. After the war, Menzies has the cryptographers destroy all traces of the project, as MI6 wants foreign governments to feel secure using their own code machines without fear of British interception. The team is instructed never to meet again or share what they have done. In 1952, Turing is convicted of gross indecency and undergoes chemical castration to be spared from prison so he can continue his work. Clarke visits him, witnesses his physical and mental deterioration, and tries to comfort him. The epilogue shows Turing committed suicide on June 7, 1954, after a year of government-mandated hormonal therapy. In 2013, Queen Elizabeth II granted him a posthumous Royal Pardon. Historians estimate that breaking Enigma shortened the war by over 2 years, saving over 14 million lives. Turing's work is now recognized as an essential step toward the development of modern computers.

The first third of the film is told from the main character's, Jean-Dominique Bauby, or Jean-Do as his friends call him, first person perspective. The film opens as Bauby wakes from his three-week coma in a hospital in Berck-sur-Mer, France. After an initial falsely positive description from one doctor, a neurologist explains that Bauby has locked-in syndrome, an extremely rare condition in which the patient is almost completely physically paralyzed, but remains mentally unchanged. At first, the viewer primarily hears Bauby's "thoughts" (he thinks that he is speaking but no one hears him), which are inaccessible to the other characters (who are seen through his one functioning eye). A speech therapist and physical therapist try to help Bauby become as functional as possible. Bauby cannot speak, but he develops a system of communication involving blinking his left eye as his therapist reads a list of letters; with this process, Bauby spells out messages one letter at a time. Gradually, the film's restricted point of view widens, and the viewer begins to see Bauby through scenes from his past as well as via the perspectives of those around him. The film shows a visit to Lourdes and conveys Bauby's fantasies about beaches, mountains, the Empress Eugénie and an erotic feast with one of his transcriptionists. We learn that Bauby had been editor of the popular French fashion magazine Elle, and that he had a deal to write a book reimagining The Count of Monte Cristo from a female perspective. He decides that he will still write a book, using his slow and exhausting communication technique. A woman from the publishing house with which Bauby had the original book contract takes dictation. The new book describes his current life, trapped in his body, which he sees as being suspended in murky water within an old-fashioned deep-sea diving bell with brass helmet, which is called a scaphandre in French. But those around him describe his still-vibrant spirit as a butterfly. The story of Bauby's writing is juxtaposed with his recollections and regrets prior to his stroke. We see his three children, their mother, his mistress, his friends, and his father. He encounters people from his past whose lives bear similarities to his own "entrapment": a friend who was kidnapped in Beirut and held in solitary confinement for four years, and his own 92-year-old father, who is confined to his own apartment, because he is too frail to descend four flights of stairs. Bauby eventually completes his memoir and hears the critics' responses. He dies of pneumonia ten days after its publication. The closing credits are accentuated by reversed shootings of breaking glacier ice (the forward versions are used in the opening credits), accompanied by the Joe Strummer & the Mescaleros song "Ramshackle Day Parade".

In 1981, San Francisco salesman Chris Gardner invests his entire life savings in portable bone-density scanners, which he demonstrates to doctors and pitches as a handy improvement over standard X-rays. The scanners play a vital role in Chris's life. While he can sell most of them, the time lag between the sales and his growing financial demands enrages his wife, Linda, who works as a hotel maid. The economic instability increasingly erodes their marriage, despite caring for Christopher Jr., their soon-to-be five-year-old son. While out on a trip to sell one of his last scanners, Chris meets Jay Twistle, a lead manager and partner for Dean Witter Reynolds and impresses him by solving a Rubik's Cube during a taxi ride. After Jay leaves, Chris skips out on paying the fare as he lacks the money, causing the driver to angrily chase him into a BART station. Despite boarding a train, Chris loses one of his scanners in the process. However, Chris' new relationship with Jay earns him the chance to become an intern stockbroker. The day before the interview, Chris begrudgingly agrees to paint his apartment for free to postpone eviction by his landlord for late rent. However, two policemen arrive to arrest Chris for multiple unpaid parking tickets. Chris has to spend the night in jail, complicating his schedule for the interview the next day. Chris narrowly arrives at Dean Witter's office on time, albeit still in shabby, paint-splattered clothes. Despite his appearance, Chris still impresses the interviewers and lands a six-month unpaid internship. He is among 20 interns competing for a paid position as a stockbroker. Chris' unpaid internship does not please Linda, who leaves for New York since she might get a job at her sister's boyfriend's new restaurant. After Chris tells Linda she is incapable of being a single parent, she leaves Christopher in Chris' care. However, Chris is further set back when his already diminished bank account is garnished by the IRS for unpaid income taxes, and Chris and Christopher are evicted. With only $21.33 in his bank account, Chris and Christopher are left homeless and desperate; Chris is able to get a motel room, but the locks are then changed when he is unable to pay on time. They are forced at one point to stay in a restroom at a BART station. Other days, Chris and Christopher spend nights at a homeless shelter, in BART, or, if Chris manages to procure sufficient cash, at a hotel. Later, he finds the bone scanner that he lost in the BART station earlier. However, Chris found it damaged, yet he still manages to repair it by selling his own blood for money availability and after that sells it to a physician, thus completing all sales of his scanners. Disadvantaged by his limited work hours and knowing that maximizing his client contacts and profits is the only way to earn the broker position, Chris develops several ways to make sales calls more efficiently, including reaching out to potential high-value customers in person, a violation of firm protocol. One sympathetic prospect, Walter Ribbon, a top-level pension fund manager, even takes Chris and Christopher to a San Francisco 49ers game, where Chris meets some of Mr. Ribbon's friends, who are also potential clients. Regardless of his challenges, Chris never reveals his lowly circumstances to his colleagues, even going so far as to lend one of his supervisors, Mr. Frohm, five dollars in his wallet for cab fare. Chris also studies for and aces the stockbroker license exam although he doubts that he did well. As Chris concludes his last day of internship, he is summoned to a meeting with the partners. Mr. Frohm lets Chris know that he has won the coveted full-time position and reimburses Chris for the previous cab ride. Fighting back tears, he shakes hands with the partners, then rushes to Christopher's daycare to embrace him. They walk down a street and joke with each other. An epilogue reveals that Chris went on to form his own multimillion-dollar brokerage firm in 1987 and sold a minority stake in it in a multi-million-dollar deal in 2006.

Henri Charrière is a safecracker nicknamed "Papillon" because of the butterfly tattoo on his chest. In France, he is wrongly convicted of murdering a pimp in 1933 and is sentenced to life imprisonment in French Guiana. On the way, he meets a fellow convict, Louis Dega, an infamous forger and embezzler. Papillon offers to protect Dega if he will fund the former's escape once they reach Guiana. Enduring the horrors of life in a jungle labour camp, the two become friends. One day, Papillon defends Dega from a sadistic guard and escapes into the jungle but is captured and sentenced to two years in solitary confinement. In gratitude, Dega has extra food smuggled to Papillon. When the smuggling is discovered, the warden screens Papillon's cell in darkness for six months and halves his rations, but Papillon refuses to give up Dega's name. He is eventually released and sent to the infirmary in St-Laurent-du-Maroni to recover. Papillon sees Dega again and asks him to arrange for another escape attempt. Dega helps him meet an inmate doctor who offers to secure a boat on the outside with the help of a man named Pascal. Fellow prisoner Clusiot and a gay orderly named André Maturette join the escape plot. During the escape, Clusiot is knocked unconscious by a guard. Dega subdues the guard and reluctantly joins Papillon and Maturette, climbing the walls to the outside. The trio meet Pascal, and they escape into the night. In the jungle the next day, Pascal delivers the prisoners to their boat, but after he leaves, the convicts discover it is fake. They encounter a local trapper who has killed the bounty hunters waiting for them. He guides the three to a leper colony, where they obtain supplies and a seaworthy boat. The trio lands in Colombia and are accosted by a group of soldiers, who wound Maturette. He is captured along with Dega, while Papillon evades the soldiers and lives for a long period with a native tribe. He awakens one morning to find them gone, leaving him with a small sack of pearls. Papillon pays a nun to take him to her convent, where he asks the Mother Superior for refuge, but instead, she turns him over to the authorities. Papillon is returned to French Guiana and sentenced to another five years of solitary confinement. He emerges a graying old man, along with Maturette, whom he sees just before the latter dies. Papillon is moved to the remote Devil's Island, where he reunites with Dega, now a farmer who has long given up hope of being released. From a high cliff, Papillon observes a cove where he realizes the waves are powerful enough to carry a man out to sea and to the nearby mainland. Papillon persuades Dega to join him in another escape, and the men make two floats from bagged-up coconuts. Dega then decides not to escape and begs Papillon not to either. Papillon embraces Dega, then leaps from the cliff and is carried out to sea. A narrator states that Papillon lived the rest of his life a free man, while the prison was closed some time before he died and ultimately reclaimed by nature.

In Laurens, Iowa, elderly Alvin Straight is found lying on his kitchen floor after a fall. His daughter, Rose, takes him to see a doctor, who admonishes him to give up tobacco, improve his diet, and use a walker, all of which he rejects. When Alvin's brother, Lyle, suffers a stroke, Alvin decides to visit him, even though they have not spoken in ten years. Lyle lives in Mount Zion, Wisconsin, 240 miles away. As neither Alvin (due to his age) nor Rose (due to an unspecified disability) has a driver's license, Alvin decides to make the trip on his riding mower. His plan surprises his family, friends, and neighbors. The mower soon breaks down, forcing Alvin to accept a ride from a passing tour bus and call for help. However, he is determined to continue the trip, and buys a used 1966 John Deere 110 lawn tractor to continue his journey. Alvin meets a variety of people on the road. He shares his dinner with a young girl hitchhiker, who ran away from home out of fear that her family would be upset with her pregnancy. Alvin reflects on the importance of family, noting how he lost half of his kids and how Rose lost custody to her children after a fire occurred in her house while she was out, later remarking that a bundle of sticks tied together is harder to break than a single one; the next day, she leaves him the former as thanks. Several passing RAGBRAI cyclists are amused to see him on the highway and welcome him to their campsite. He speaks with some of the cyclists about growing old. He also meets a distraught woman who hit a deer during her commute and tearfully rants about how she repeatedly hits deer despite her prayers. Alvin respectfully cooks and eats the deer. Alvin's tractor begins to fail, throwing his journey into jeopardy. His transmission fails as he travels down a steep hill, but he manages to stop. Danny, a local, invites Alvin to camp in his backyard until the tractor is repaired. He offers to drive Alvin to Mount Zion, but Alvin declines, preferring to travel his own way. Running low on cash, Alvin calls Rose to send him his Social Security check. Two bickering local mechanics overcharge him for fixing his tractor, but he cannily bargains the price down. A fellow veteran invites Alvin for a drink, and they exchange traumatic stories about their experiences in World War II. Alvin, a sniper during the war, declines a beer but confesses that he is still haunted by killing an American in a friendly fire incident, becoming an alcoholic when he returned home but is now sober. After crossing into Wisconsin, Alvin chats with a Catholic priest who knows of Lyle and his stroke. The priest states that Lyle never mentioned a brother; Alvin admits that he wants to make amends. Although the exact cause of the brothers' estrangement is never stated, Alvin says that anger, vanity and alcohol were involved. Alvin finally arrives in Mount Zion. To steel himself, he drinks his first beer in years. His tractor stalls just short of Lyle's dilapidated cabin, but he persists. Lyle invites Alvin to sit together on the porch; asking if Alvin rode the tractor all the way just to see him. Alvin quietly confirms this as Lyle's eyes well up with tears. The two men sit together silently and gaze up at the stars.