The Kuiper belt is a region beyond Neptune that is full of comets, asteroids and other debris. It circles the solar system and has always been a little bit of a mystery as it is so far away and hard to explore.
The inkling that the Kuiper belt existed first came from Kuiper and a British scientist called Edgeworth who both theorised about the Kuiper belt but it took a lot of time for the first Kuiper Belt object to be seen.
The Kuiper belt was thought to exist beyond Neptune because the layout of the solar system from Jupiter to Neptune showed a decrease in planetary mass which implied that beyond Neptune there was unaccounted material. This could only be either small planets or a lot of small celestial bodies.
Also, odd celestial body orbits were found, for instance Chiron in 1977, that crossed the orbit of Saturn. These objects, called centaurs (objects that pass the orbits of the giant planets) were thought to have short lifespans because of the possibility of an impact with the giant planets. This meant that there must be a supply of centaurs and that they had suffered orbital evolution after originating from the Kuiper belt similar to Short period comets that were also observed. In 1992 the object QB1 was found by astronomers, the first of several hundred which are known today.
Kuiper belt objects are sorted into three different classes called dynamical groups. Plutinos, the first of the classes, are in a stable resonance of 3:2 with Neptune and are therefore locked into their orbits which creates no interaction with the solar system planets.
The next class of Kuiper belt objects are called classical objects or Cubewanos that have a large distance from the Sun normally greater than 42AU and small eccentricities creating roughly circular orbits close to the plane of the ecliptic. Most do not interact with the terrestrial planets or gas giants because of their distance and circular orbits.
The last Kuiper Belt objects are scattered disc objects which have larger eccentricities and distances from the Sun greater than 100AU. Their orbits take them well above and below the ecliptic plane in orbits similar to centaurs and therefore their orbits can change and impacts can occur due to a gas giants gravity.
Because Kuiper belt objects are so faint and move very little compared to the background of stars visual instruments are unable to see them as discs and therefore are unable to work out their size although the Hubble space telescope has imaged a few Kuiper belt objects.
Therefore information about the Kuiper belt has been gained by other techniques such as a lightcurve. Light is reflected from the body which gives us the cross-sectional area of the side lit by the Sun. This causes a changing brightness which gives us the spin rate (from the period of the light curve) and the ratio of the longest to shortest side(amplitude) giving us information about its shape.
The reflectance spectrum can also give us some information. Give us the relative efficiency with which a body reflects sunlight. This is not the albedo as we do not know how big the object actually is but it can tell us whether the body has a neutral reflectance spectrum reflecting all the sunlight equally or that it reflects light more efficiently at longer wavelengths which would give a red appearance. From this information we can tell how the surface of a body changes and therefore predict its surface properties.
Unfortunately we know very little about the Kuiper belt because of its distance and movement of its objects against the background stars. A NASA mission called New Horizons is on its way to Pluto and the Kuiper belt and maybe able to give us more detailed information in the future.