A widespread catastrophic crop blight on Earth has made farming increasingly difficult and threatens the existence of humanity. Joe Cooper (McConaughey), a widowed former NASA pilot, runs a farm with his father-in-law Donald, son Tom, and daughter Murphy. Murphy believes her bedroom is haunted by a poltergeist. When the "ghost" creates a pattern of dust on the floor, Cooper realizes an unknown intelligence is using gravity to communicate, and interprets the pattern as geographic coordinates, which Cooper and Murphy follow to a secret NASA facility.
There, they meet Dr. Brand (Michael Caine), a college professor of Cooper's. Brand reveals that a wormhole, apparently created by an alien intelligence, appeared near Saturn 48 years before and leads to a distant galaxy, 10 billion lightyears from Earth and the Milky Way, with numerous potentially habitable planets. Twelve volunteers have gone through it, knowing they were unlikely to be able to return, each to assess a different planet's suitability as a new home for humanity. Three – Miller, Edmunds and Mann – have sent encouraging data from planets near Gargantua, a supermassive black hole. Brand recruits Cooper to pilot the spacecraftEndurance to evaluate as many of the planets as possible, while he works on "Plan A", a theory to harness gravity for propulsion, which would allow humanity to leave Earth. However, should his efforts fail, the Endurancealso carries 5,000 frozen embryos as "Plan B", to provide for humanity's survival. Cooper agrees to the plan, angering Murphy.
Cooper's crew consists of three scientists – Romilly, Doyle, and Brand's daughter Amelia – and robots TARS and CASE. Traversing the wormhole, they first head to Miller's planet, an ocean world where time is severely dilated due to the proximity to Gargantua; for each hour there, seven years pass on Earth. While Romilly and TARS stay on the Endurance, the rest take a lander to the surface, where they find wreckage of Miller's lander. Brand and Doyle venture out further, attempting to retrieve the craft's black box. Cooper realizes that the land in front is not mountains but instead, a giant wave. The tidal wave strikes, killing Doyle and waterlogging the lander's engines. By the time Cooper, Amelia, and CASE return to Endurance, 23 years have elapsed back on Earth.
Murphy, now an adult, has been assisting Dr. Brand with his research. On his deathbed, he admits to her that he solved the gravity equation long before and deemed Plan A impossible, and that he lied to everyone, pinning his hopes on Plan B. Murphy notifies Amelia of her father's death, then accuses her and Cooper of abandoning Earth. She continues the research, believing Plan A might work if they could get more data regarding Gargantua's singularity.
With limited fuel, Cooper decides to go to Mann's planet, rather than Edmunds', as Mann has been transmitting promising data. After being revived from cryosleep, Mann assures the crew that while the frozen planet has an ammonia-laden atmosphere, the planetary surface is fit for human survival. However, when they are alone, Mann attempts to kill Cooper, revealing that he falsified the data so he would be rescued. Mann then flees, intending to take the Endurance. Meanwhile, Romilly is killed by a booby trap Mann had set inside his own robot.
Amelia rescues Cooper, and they race to the Endurance, where Mann is attempting to dock despite a lockout of the autodocking system put in place by Cooper. Mann defies Cooper's order not to open the airlock, which fails catastrophically. Mann is killed and theEndurance is severely damaged and begins to fall into the planet. Cooper manages to use the landing craft to stabilize the ship. Using Gargantua's gravity as a slingshot, they set the ship on course to Edmunds' planet; but being close to a black hole, 51 years would pass on Earth.
To shed weight, Cooper jettisons himself and TARS into the black hole, so that Amelia and CASE can complete the journey. Cooper and TARS plunge into the black hole, but emerge in a tesseract, which appears as a stream of bookshelves; with portals that look out into Murphy's bedroom at different times in her life. Cooper realizes that the tesseract and wormhole were created by fifth dimensional beings from the future to enable him to communicate with Murphy through gravitational waves, and that he is her "ghost". He relays quantum data that TARS collected from the black hole in Morse code by manipulating the second hand of a watch he gave to Murphy before he left. Murphy uses the quantum data to solve the remaining gravitational equation, enabling Plan A.
Cooper emerges from the wormhole and is rescued by the crew of a space habitat orbiting Saturn. Aboard, he reunites with Murphy, now elderly and near death. After sharing one last goodbye, Cooper, along with TARS, leaves the habitat to rejoin Amelia, who is with CASE on Edmunds' Planet, which was found to be habitable.