Amelia Earhart was a 20th century female pioneer of Human aviation. She was an accomplished pilot, setting various world records. In 1937, during her attempt to circumnavigate Earth, Earhart and her navigator, Fred Noonan, disappeared. (ENT: "Terra Nova"; VOY: "The 37's")
Many people spent decades trying to figure out the mystery of what happened to Earhart. However, according to Travis Mayweather, the mystery of her appearance, as well as the mysterious disappearance of Judge Crater did not hold a candle to the disappearance of the Terra Nova colony over a century later. (ENT: "Terra Nova")
There were several theories surrounding the disappearance of the two, such as: she and Noonan were lovers and ran away together, she had been abducted by aliens, and that she had been shot down or captured by the Japanese. The commonly accepted theory was, though, her plane simply crashed from lack of fuel.
Unknown at the time, Earhart, Noonan and six other Humans were abducted by an alien race known as the Briori and transported to the Delta Quadrant. They would be placed in a stasis chamber, and over a period of four centuries, become known to the planet's inhabitants – Humans descended from other abductees, who had overthrown their Briori captors – as "the 37's".
In 2371, after tracing an SOS call to her still-intact plane (preserved by a Briori power source), the crew of the USS Voyager discovered Earhart, Noonan and the six other 20th century Humans still in cryostasis in caves on an Earth-like planet in the Delta Quadrant. After being woken up, Earhart, along with Noonan and the others, declined Captain Janeway's offer to remain on board and decided to stay on the planet with the thriving Earth-like civilization that their fellow Humans had established there. (VOY: "The 37's")