Triton
      Triton (TRY-tun) is Neptune's largest moon. It has a very thin nitrogen atmosphere, with a surface pressure estimated to be 10 or 20 millionths of the Earth's atmospheric pressure. The mostly water-ice surface has many large cracks, probably caused by partial melting of the interior, and ice geysers spew nitrogen gas and dark, presumably carbon-rich particles several miles into the thin atmosphere. Winds then blow the gas sideways, forming dark plumes. In comparison to most other moons there is a relative dearth of cratering, indicating considerable geological activity, albeit in ice rather than in rock, continuing to the present day.
      Triton's orbital motion is retrograde (opposite the rotation of Neptune). It is the only large moon in the solar system to have such an orbital motion, and it is suspected that the odd orbital motions of Triton and Nereid are probably related to near-collisions or captures early in the history of the solar system. If Triton was captured into an eccentric orbit and tidal friction converted it to the currently nearly circular orbit, a substantial portion of its original ice could have melted and evaporated, and large portions have been lost, giving it the higher than average density it has.
      Future tidal friction caused by its retrograde revolution will gradually reduce the size of Triton's orbit, and in the distant future -- perhaps a hundred million years or so -- it may well be torn to pieces by Neptune's gravity, producing a ring system similar to the one that Saturn has.
      The evaporation and refreezing of gases give Triton a relatively high albedo. Between that and its great distance from the Sun Triton absorbs very little heat, and has the lowest temperatures measured for any solar system object to date.

Proteus
      Proteus (PRO-tea-us) is the second largest of Neptune's moons, but wasn't discovered until Voyager 2 swept by Neptune in 1989, because it is very close to Neptune and is one of the darkest moons in the solar system, reflecting only 6% of the sunlight which falls upon it. It is relatively round, but for such a large object (about 260 miles average diameter) is somewhat irregular in shape. It is heavily cratered, and presumably little changed since the formation of the solar system.

Nereid
      Nereid (NEAR-ee-id) is the third largest of Neptune's moons, but is notable and unique among all the planets and moons in the solar system as a result of its orbit. Usually satellite orbits are relatively circular, but Nereid's orbit has an eccentricity of 0.75, meaning that its distance varies by up to 75% from the average. As a result at periapsis it is more than seven times closer to Neptune than at apoapsis. Other than that and the fact that it is a little over 200 miles in diameter, very little is known about the outermost of the larger Neptunian moons.

Smaller Moons of Neptune
Inner Moons discovered by Voyager 2 (1989): (works in progress)
     The five small moons discovered by Voyager 2 all lie inside the synchronous orbital distance. That is, they all orbit Neptune in less time than it takes to rotate. As a result, tidal interactions gradually slow the orbital motion, causing the orbit to slowly spiral inward (and as a result actually orbiting faster than before). Eventually all these moons will be pulled apart by Neptune's gravity (once inside its Roche limit) or enter its outer atmosphere, and in either case, disintegrate.
     Naiad is the closest known moon to Neptune.
     Thalassa is the second closest moon to Neptune.
     Despina is the third closest moon to Neptune.
     Galatea is the fourth closest moon to Neptune.
     Larissa (la-RISS-sa) is the fifth closest moon to Neptune.
Outer Moons discovered by Terrestrial observations:
     The five moons discovered in 2002 and 2003 are all small "irregular" moons. This does not mean that they have irregular shapes (though they may), but that their orbits are very large, relatively eccentric and/or highly inclined, and as often as not in retrograde revolution (backwards relative to the rotation of the planet instead of in the same direction as the rotation, which is referred to as direct or prograde revolution).
     These moons are all assumed to have albedos around 4%, typical of dirty snowballs in the outer solar system, and average densities between 1 and 2 times the density of water. Their diameters are estimated from a comparison of their brightness to the brightness expected for objects of 4% albedo, and their masses are calculated from their estimated diameters and densities. Since their albedos and densities are merely educated guesses, their actual sizes and masses are unknown.
     S/2002 N1 Halimede (HAL-ih-MEE-dee)
     S/2002 N2 Sao (SAY-oh)
     S/2002 N3 Laomedeia (LAY-o-meh-DEE-uh, or LAY-o-meh-DYE-uh)
     S/2002 N4 Neso (NEE-soh)
     S/2003 N1 Psamathe (SAM-uh-thee)