The Voyager crew discovers that a group of people on Earth who disappeared in the 1930s, including Captain Kathryn Janeway's personal hero Amelia Earhart and her navigator Fred Noonan, were in fact captured by aliens and brought to a planet in the Delta Quadrant for slave labor. This group were dubbed "The 37s".
For unspecified reasons, half a dozen individuals including Earhart and Noonan were placed in cryostasis while other people from Earth rebelled against their alien captors, destroying them and their orbiting vessel.
When Voyager's crew comes upon the planet in the 24th Century, the 37s have been left in stasis for centuries and the descendants of the original Terran abductees have developed several cities on the planet's surface using fusion-based technology left by their captors. Earhart and Noonan (and the others) are revived and Earhart is given a tour of the Voyager, learning about her place in history. When offered a chance to join the Voyager crew, Earhart and Noonan decline, deciding to stay on their adopted homeworld.
The episode makes numerous references to the Earhart legend, adding one element; in this version of the story it is revealed that Noonan has fallen in love with his pilot, and romance blossoms between the two as they choose to stay on the planet.
In the end, all of the 37s decide to remain on the planet. Despite being offered the opportunity to settle on the Earth-like planet, every member of the Voyager crew declines and resume their journey home.