In a prehistoric veld, a tribe of hominins is driven away from its water hole by a rival tribe. The next day, they find an alien monolith has appeared in their midst. The tribe then learn how to use a bone as a weapon and, after their first hunt, return to drive their rivals away with it.
Millions of years later, Dr Heywood Floyd, Chairman of the United States National Council of Astronautics, travels to Clavius Base, an American lunar outpost. During a stopover at Space Station Five, he meets Russian scientists who are concerned that Clavius seems to be unresponsive. He refuses to discuss rumours of an epidemic at the base. At Clavius, Heywood addresses a meeting of personnel to whom he stresses the need for secrecy regarding their newest discovery. His mission is to investigate a recently found artefact, a monolith buried four million years earlier near the lunar crater Tycho. As he and others examine the object and are taking photographs, it emits a high-powered radio signal.
Eighteen months later, the American spacecraft Discovery One is bound for Jupiter, with mission pilots and scientists Dr Dave Bowman and Dr Frank Poole on board, along with three other scientists in suspended animation. Most of Discovery's operations are controlled by HAL, a HAL 9000 computer with a human-like personality. When HAL reports the imminent failure of an antenna control device, Dave retrieves it in an extravehicular activity (EVA) pod, but finds nothing wrong. HAL suggests reinstalling the device and letting it fail so the problem can be verified. Mission Control advises the astronauts that results from their backup 9000 computer indicate that HAL has made an error, but HAL blames it on human error. Concerned about HAL's behaviour, Dave and Frank enter an EVA pod so they can talk in private without HAL overhearing. They agree to disconnect HAL if he is proven wrong. HAL follows their conversation by lip reading.
While Frank is floating away from his pod to replace the antenna unit, HAL takes control of the pod and attacks him, sending Frank tumbling away from the ship with a severed air line. Dave takes another pod to rescue Frank. While he is outside, HAL turns off the life support functions of the crewmen in suspended animation, killing them. When Dave returns to the ship with Frank's body, HAL refuses to let him back in, stating that their plan to deactivate him jeopardises the mission. Dave releases Frank's body and opens the ship's emergency airlock with his remote manipulators. Lacking a helmet for his spacesuit, he positions his pod carefully so that when he jettisons the pod's door, he is propelled by the escaping air across the vacuum into Discovery's airlock. He enters HAL's processor core and begins disconnecting most of HAL's circuits, ignoring HAL's pleas to stop. When he is finished, a prerecorded video by Heywood plays, revealing that the mission's actual objective is to investigate the radio signal sent from the monolith to Jupiter.
At Jupiter, Dave finds a third, much larger monolith orbiting the planet. He leaves Discovery in an EVA pod to investigate. He is pulled into a vortex of coloured light and observes bizarre astronomical phenomena and strange landscapes of unusual colours as he passes by. Finally he finds himself in a large neoclassical bedroom where he sees, and then becomes, older versions of himself: first standing in the bedroom, middle-aged and still in his spacesuit, then dressed in leisure attire and eating dinner, and finally as an old man lying in bed. A monolith appears at the foot of the bed, and as Dave reaches for it, he is transformed into a foetus enclosed in a transparent orb of light floating in space above the Earth.
