First of all, as an enthusiastic internet space buff, I'm excited to tell you that, much like Britain's royal family, our solar system has a new member. Neptune has had a moon. Ok, the moon itself isn't new, obviously. We just now found it though! It doesn't have a name yet and as heavenly bodies go, it is really a baby, only 20 km across. But it's number 14 in Neptune's satellite family and part of what's interesting about it is how it was discovered.
Neptune itself was discovered using math, not telescopes. In 1846, French mathematician Urbain Le Verrier, or something like that, noticed aberrations in the orbit of Uranus and applying what he knew about physics, concluded that there had to be another planet nearby that was changing its path. When astronomers pointed their telescopes to where Le Verrier predicted, there it was. But Neptune's new moon, even though it's 1/2500th the size of the planet, was found using even more traditional astronomical devices: eyeballs.
Mark Showalter of the SETI Institute in Mountain View, California, found it while reviewing archival photographs taken by the Hubble Space Telescope. So yes, his eyes did have the help of the most powerful telescope known to humanity and also some computer software. But while studying the images of Neptune taken between 2004 and 2009, Showalter noticed a bright spot that occurred periodically far outside the planet's rings. After plotting out the path of the spot, he found that it made a circular orbit around Neptune once every 23 hours.
This isn't Showalter's first discovery either. He's found moons around Saturn, Uranus, and Pluto. He's also become an expert at naming these things. As discoverer of the new body, he gets to submit possible names to the International Astronomical Union, which will decide its official moniker. Since the parent planet is Neptune, the name has to relate to the Greek or Roman gods of the sea, and Showalter says he already has a couple of nominees: Polyphemus, the son of Poseidon who guest starred as the Cyclops in Homer's The Odyssey or Lamia, Poseidon's daughter who was busted for having an affair with Zeus and was punished by being turned into a monster that feeds on children. Or you could try to name it, in the comments. They won't take those into consideration though.