On April 3, 2005, the NDR series robot "Andrew" is introduced into the Martin family home to perform housekeeping and maintenance duties and introduces himself by showing a presentation of the Three Laws of Robotics. The eldest daughter Grace despises Andrew, but her younger sister Amanda is sympathetic to him, and Andrew discovers he feels emotions, and is drawn to spend more time with his "Little Miss". He accidentally breaks one of her glass figurines and is able to carve a new one out of wood, which surprises her father Richard. Richard takes Andrew to NorthAm Robotics to inquire if Andrew's creativity was part of his programming. NorthAm's CEO Dennis Mansky claims this is a problem and offers to scrap Andrew, but instead Richard takes Andrew back home and encourages him to continue his creativity and explore other humanities. Andrew becomes a clockmaker and earns a sizable fortune managed by Richard after they find that robots have no rights under current laws. In 2020, Richard encourages Dennis to retrofit Andrew with the ability to present facial expressions to match his emotions. In 2032, Andrew presents Richard with all the money he has made to ask for his freedom. Wounded by this, Richard refuses but grants Andrew his independence on the condition that he may no longer reside at the Martin home. Andrew builds his own home by the beach. In 2048, Richard is on his death bed, and apologizes to Andrew for banishing him all those years ago. Following Richard's death, Andrew goes on a quest to find other NDR robots that are like him, frequently communicating back to Amanda, who has since married and divorced, and has a son Lloyd and granddaughter Portia. In 2068, Andrew discovers Galatea, an NDR robot that has been modified with a female personality and traits. Andrew becomes interested in how Galatea was modified by Rupert Burns, the son of the original NDR designer, and finds he has a number of potential ideas to help make robots appear more human-like. Andrew agrees to fund Rupert's work and to be a test subject and is soon given a human-like appearance. Andrew finally returns to the Martin home and finds that Amanda has grown old while Portia looks much like her grandmother at her age. Portia is initially cautious of Andrew, but soon accepts him as part of the Martin family. When Amanda dies, Andrew realizes that all those he cares for will also pass on. He presents ideas to Rupert to create artificial organs that not only can be used in humans to prolong their lives but also to replace Andrew's mechanical workings. Andrew gains the ability to eat, feel emotions and sensations, and even have sexual relationships, resulting in him and Portia falling in love. Andrew petitions the World Congress to recognize him as a human as to allow him to marry Portia, but the body expresses concern that an immortal human will cause jealousy from others. Many years later when Portia is nearly 75 years old, Andrew returns to Rupert for one last operation: to change the artificial fluids driving his body into a blood equivalent. Rupert cautions him that the blood will not last forever, causing his body to age and will die eventually, a fate Andrew accepts. An unknown amount of years later, a now visibly aged Andrew again approaches the World Congress, with Portia as support, to appeal their past decision, wanting to be able to die with dignity. On April 2, 2205, with Andrew's body deteriorating, he and Portia are both under life support monitored by Galatea, now with a human appearance. They hold hands and watch the World Congress as they recognize Andrew as a human being, the world's oldest at 200 years, and giving all rights confirmed by that, including validating his marriage to Portia. Andrew dies during the broadcast, which is confirmed by Galatea while Portia asserts that Andrew already knew the answer. After ordering Galatea to turn off her life support, Portia soon dies, hand-in-hand with Andrew as she whispers to him "See you soon".

When Alice arrives unannounced at her estranged brother Ethan's house in an attempt to reconcile, bizarre visions and the return of Ethan's strange girlfriend, Misty, begin to spark paranoia and suspicion. As the haunting visions become more peculiar, the two siblings desperately cling to reality, but are forced to face the mysterious circumstances.

Ray, recently fired from his job as a theme park guide, spends the evening with his friends Pete and Toby at the cinema and later at a pub. There, they write a satirical "Letter to Hollywood" criticising bad films, using a page from Toby’s notebook. Ray encounters a woman named Cassie, who claims to be a time traveller working to fix "time leaks." She warns him about "Editors," operatives from the future who eliminate artists at their peak to preserve cultural standards. Ray believes the encounter is a prank arranged by his friends; they deny it and think he is making up meeting Cassie. Soon after, Pete experiences a bizarre vision of a massacre at the pub, including a bearded version of himself. The group discovers a time leak in the men's toilet, which allows them to travel 30 minutes into the past and encounter earlier versions of themselves. Cassie returns, stating she has repaired the leak, but anomalies continue to occur. They enter a post-apocalyptic version of the pub, and Pete briefly disappears into the time leak, returning dishevelled and traumatized. The group attempts to avoid paradoxes caused by interacting with their past selves. During a party at the pub that is themed around their future selves, they meet Millie, another time traveller who claims to be Cassie's mentor but is later revealed to be an Editor sent to kill them at the moment of their greatest potential. Believing the "Letter to Hollywood" may be responsible for their future fame, Ray, Pete, and Toby consider destroying it to prevent Millie’s interference. Millie incapacitates Cassie and offers to make them legends in exchange for the paper, but they refuse. A confrontation ensues, and Millie appears to kill everyone in the pub. An earlier version of Pete enters, witnesses the aftermath, and flees. A severely injured Ray spills beer on the paper, rendering it illegible. This act triggers a reset of the timeline, returning the trio to their original state at the pub, with full memories of the events, but with the paper destroyed. As they leave, believing the situation resolved, Cassie reappears through a portal, now claiming she and Ray have been in a relationship in an alternate timeline. She warns of widespread time leaks and urges them to help save the world within fourteen hours. The group agrees to follow her into a parallel universe. In mid- and post-credits scenes, multiple versions of Pete and Toby appear, suggesting ongoing complications from the time travel events.