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Nasa
As of now, there are no approved missions to revisit Neptune anytime soon. New technology could make a mission in the 2030s worthwhile, but currently, any incentive to visit Neptune pails in comparison to the amount of resources and time it would take to reach the planet again. That being said, our first and only mission (Voyager 2) has provided us with almost all our information about the planet known today.
Wikimedia
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Voyager 2 is the only spacecraft to come close to Neptune. The Probe reached Neptune on August 24th, 1989, taking images of the planet and the moon Triton. In addition, it also took images of never-before-seen cloud patterns and faint bands seen on the surface of the planet.
First image of Triton from Voyager 2
New moons Laomedia, Neso, Sao and Halimede discovered in 2002
Discovery of Psamathe a new moon in 2003
Accidental finding of a unknown moon formally called S/2004 N 1
Wikimedia Picture of Neptune by voyager 2
For Neptune the main reason for the lack of exploration is because the gas giant is very far away, meaning that if we wanted to explore it more it would be complicated and costly to send expeditions out there. Neptune is between 2.7 billion miles and 2.9 billion miles from Earth depending on its orbit meaning if we were to send something to document the planet it would need extensive research to survive cold, low light. It would take between 8 and 18 years to travel to the planet depending on when it is launched and how its speed it increased.