In the future, crop blight has caused civilization to regress into a failing agrarian society. Former NASA pilot Cooper runs a farm with his father-in-law, his teenage son, and his 10-year-old daughter Murphy. Murphy believes her room is haunted by a ghost trying to communicate with her. She and Cooper discover the "ghost" is an unknown intelligence sending coded messages using gravitational waves, leaving binary coordinates in the dust that direct them to a secret NASA installation led by Professor John Brand. Brand reveals that a wormhole, created by an alien intelligence, leads to new planets that may offer hope for survival. NASA's "Lazarus missions" have identified three potentially habitable worlds orbiting the black hole Gargantua: Miller, Edmunds, and Mann, named after the astronauts who surveyed them. Brand recruits Cooper to pilot the spacecraft Endurance to recover the astronauts' data; if one of the planets is habitable, humanity will follow on space stations. Cooper's departure devastates Murphy, and they part on bad terms.
On Endurance, Cooper joins Brand's daughter, biologist Amelia; scientists Romilly and Doyle; and robots TARS and CASE. They enter the wormhole and head to Miller, but discover the planet is so close to Gargantua that it experiences severe gravitational time dilation: each hour on the surface is seven years on Earth. They descend to the planet, which proves inhospitable as it is covered by a shallow ocean roiled by enormous tidal waves. As Amelia attempts to recover Miller's data, a wave hits, killing Doyle and delaying the shuttle's departure. When Cooper and Amelia return to Endurance, 23 years have passed.
On Earth, the adult Murphy is now a NASA scientist assisting Brand with the equation that will enable NASA to launch its massive space stations via gravity. On his deathbed, Brand admits he already solved the problem and determined the project is impossible; he covered up his findings and put his faith in a "Plan B": using fertilized embryos to start humanity anew. However, Murphy concludes that Brand's equation could work with additional data from a black hole's singularity.
Low on fuel, Endurance can only visit one more planet before returning to Earth. Amelia suggests that next destination be Edmunds but Cooper disagrees on the basis that this might be an emotional decision for amelia as she loves Edmunds. In this conversation Amelia suggest love as a demonstration of force from higher dimension but no one agrees with her. The team finally selects Mann's planet, as Mann is still transmitting. However, they find it to be icy and inhospitable; Mann always knew Plan B was the mission's true goal, and faked data about his planet's viability so Endurance would rescue him. Mann breaks Cooper's spacesuit visor and leaves him to die, and flees to Endurance on a shuttle; Romilly is killed by a bomb Mann set to protect his secret. Amelia rescues Cooper on the other shuttle, and they arrive at Endurance in time to witness Mann docking improperly. The airlock explodes, killing Mann and causing serious damage, but Cooper uses the shuttle to get Endurance under control.
Nearly out of fuel, Cooper and Amelia plan to slingshot Endurance around Gargantua on a course toward Edmunds. TARS and Cooper detach into the black hole, sacrificing themselves to collect data on the singularity and to propel Amelia by dropping the ship's mass. They emerge in an extra-dimensional "tesseract", where time appears as a spatial dimension and portals show glimpses of Murphy's childhood bedroom at various times. Cooper realizes the alien beings may be future humans and have constructed this space so he can communicate with Murphy and save humanity. Using gravitational waves, Cooper encodes TARS's data on the singularity into the adult Murphy's watch, allowing her to solve Brand's equation and evacuate Earth. The beings then close the "tesseract" and Cooper is ejected from Gargantua back into the Solar System near Saturn. Due to the time dilation from the entire mission, humans have evolved to become an advanced spacefaring race at this point -- a space police vehicle finds Cooper near Saturn before his oxygen exhausts. Cooper awakens later aboard of NASA's "Cooper Station" and reunites with the now elderly Murphy, who has led humanity's exodus. Murphy advises Cooper and TARS to search for Amelia, who has begun preparation on Edmunds's planet.