In both the book and the movie, the story is set nine years after the failure of the Discovery One mission to Jupiter. A joint Soviet-American crew, including Heywood Floyd from 2001, on the Soviet spaceship Alexei Leonov (named after the famous cosmonaut) arrives to discover what went wrong with the earlier mission, to investigate the monolith in orbit around the planet, and to resolve the disappearance of David Bowman. They hypothesize that much of this information is locked away on the now-abandoned Discovery One. The Soviets have an advanced new "Sakharov" drive which will propel them to Jupiter ahead of the American Discovery Two, so Floyd is assigned to the Leonov crew.
However, a Chinese space station rockets out of Earth orbit, revealing itself to be the interplanetary spacecraft Tsien, also aimed at Jupiter. The Leonov crew members think the Chinese are on a one-way trip due to its speed, but Floyd surmises that due to the large water content of Europa they intend to land there and use the water content to refuel. The Tsien's daring mission ends in failure, when it is destroyed by an indigenous life-form on Europa. The only survivor radios the story to the Leonov; it is presumed that he dies when his spacesuit air supply runs out.
The Leonov survives a dangerous aerobraking around Jupiter and arrives at Discovery. Mission crewmember and HAL 9000's creator, Dr. Chandra, reactivates the computer to ascertain the cause of his earlier aberrant behavior.
A sequence of scenes follows the explorations of David Bowman, who has been transformed into a non-corporeal, energy-based life-form, much like the aliens controlling the monoliths. During his journey, the avatar of Bowman travels to Earth, making contact with significant individuals from his human past: He visits his mother and brushes her hair (shortly before she dies), and he appears to his ex-girlfriend on her television screen. In the novel, the aliens are using Bowman as a probe to learn about humankind. He then returns to the Jupiter system to explore beneath the ice of Europa, where he finds aquatic life-forms, and under the clouds of Jupiter, where he discovers gaseous life-forms. Both are primitive, but the aliens deem the Europan creatures to have evolutionary potential.
An apparition of Bowman appears before Floyd, warning him that they must leave Jupiter within 15 days. Floyd has difficulty convincing the rest of the crew at first, but then the monolith vanishes from orbit and a mysterious dark spot on Jupiter begins to form and starts growing. HAL's telescope observations reveal that the "Great Black Spot" is, in fact, a vast population of monoliths, increasing at a geometric rate, which appear to be eating the planet.
The Leonov crew devises a plan to use the Discovery as a "booster rocket", enabling them to return to Earth ahead of schedule. Unfortunately, HAL and the Discovery will be trapped in Jupiter's orbit, with insufficient fuel to escape. The crew are worried that HAL will have the same neuroses on discovering that he will be abandoned yet again, and Chandra must convince HAL that the human crew is in danger.
The Leonov crew flees Jupiter as the swarm of monoliths spread to engulf the planet. Through a mechanism the novel only partially explains, these monoliths increase Jupiter's density until the planet achieves nuclear fusion, becoming a small star. In the novel, this obliterates the primitive life forms inhabiting the Jovian atmosphere, which the Monoliths' controllers had deemed less worthy than the aquatic life of Europa.
As Jupiter is about to transform, Bowman returns to Discovery to give HAL a last order to carry out. HAL begins repeatedly broadcasting the message "ALL THESE WORLDS ARE YOURS EXCEPT EUROPA. ATTEMPT NO LANDINGS THERE." The creation of the new star, which Earth eventually names Lucifer, destroys Discovery. However, HAL's artificial intelligence is removed from Discovery's computer core and transformed into the same kind of life form as David Bowman, and becomes his companion.