Kelvan agents from the Andromeda Galaxy captured the Enterprise to carry them home, until their new human senses gave the crew a way to retake the ship.
In 2268 the Enterprise answered a distress call and was taken by a group of Kelvans, beings from the Andromeda Galaxy whose home was threatened. They had taken human form to run the ship and turned most of the crew into small solid blocks, and they modified the Enterprise to travel to Andromeda on a centuries-long journey. The ship crossed the galactic barrier.
The Kelvans were not used to human feelings, and the crew used this against them, with Kirk stirring jealousy and Scott getting one drunk. The Kelvan leader Rojan finally agreed to settle peacefully on a planet in the Milky Way.