While there are probably millions of small bodies orbiting the Sun outside the orbits of Neptune and Pluto, it is very difficult to see lots of them because they are tiny, only around 20km across. Some small bodies enter the inner solar system as comets. In 1950, Jan Oort proved that these didn't come from outside the solar system, but from the outer reaches.
The Kuiper Belt
The Kuiper Belt lies outside the orbit of Neptune, around 30 to 100AU out from the Sun. It is disc-shaped, and thought to be the source of short period comets1. Most Kuiper Belt objects are very small, and only a very few observations of them have been made. However, some astronomers believe that there are two other Kuiper belt objects that we know more about - Neptune's satellite Triton and the dwarf planet Pluto.
When Kuiper Belt objects interact with the planet Neptune, one of three changes occurs. The objects may be sent out of the solar system altogether; they may start to orbit in the area of the other gas giants; or they may be sent into the inner solar system. Many comets thought to originate in the Kuiper Belt have orbits such that they never get close to Neptune - they are said to have resonant orbits.
The Oort Cloud
When Jan Oort studied where comets came from, he observed that they seem to come equally from all directions. (This isn't quite true, but we'll come to this later.) By their paths, they should originate in a region 20,000 to 100,000AU from the Sun2. This region, if it exists, is called the Oort Cloud. We have no observational data from that region because it is so very far away. We cannot tell if there really is an Oort Cloud as yet. However the idea raises many questions. As it is so far away, the pull of gravity from the Sun shouldn't be enough to keep it there. If the Oort Cloud is there, why do comets come in closer to the Sun?
Every few million years, the Sun will pass close to another star. A million years from now the star Gliese 710 will pass within a light-year of the Sun; encounters like this should strip the Oort Cloud away from the solar system. The Oort Cloud is too far out to have been formed the same way the planets were. It is also spherical, and everything else in the solar system is disk shaped. If this cloud exists, then somehow the Sun must lose Oort Cloud objects and gain them, but we don't know how.
Planet X or Nemesis?
Dr John Murray recently went back through records of the paths of long period comets. He noticed that Jan Oort was wrong - they don't come from all areas of the Oort Cloud equally. There is a region about 30,000 to 50,000AU away which produces more than its fair share of comets. He speculated that a Planet X, moving through the Oort Cloud about 40,000AU away, scattering other Oort Cloud objects in all directions, might cause this. Dr Murray thought the planet should be one to ten times the mass of Jupiter. However Dr John Matese came to the Planet X conclusion independently, and thinks the planet should be bigger - about brown dwarf (that is, a failed star) size. If this is the case it raises interesting questions, including how did it get there? It is much too far out to have been formed the way the other planets were.
The Nemesis theory was suggested to explain why comets get sent in toward the Sun. Most stars are part of a binary system, but is our Sun as well? Every 20 or 30 million years or so, mass extinctions seem to occur on Earth. Suppose the binary companion of the Sun is very faint and on a highly elliptical orbit, passing through the Oort Cloud every 20 million years, diverting comets into the inner Solar System, causing meteor bombardments of the planet Earth, and making species become extinct.
This theory is not widely accepted; the evidence for it is extremely tenuous. But it illustrates how very little we really do know about the extremes of our Sun's system.
The Truth is Out There
Many people are studying the problems raised by the outside of the solar system. Recently a group of American astronomers has been trying to work out how often the Moon is hit by meteorites. They realised that every time a meteor hits the Moon, it must send up a lot of dust, which then spreads out over the Moon's surface. When the Apollo missions brought back Moon dust, they would have brought back evidence of meteor hits too. They noticed that although there were lots of meteorite hits when the moon was very young, the number decreased until about 400 million years ago, when it got higher. It has remained high ever since. Something must have happened to send more comets into the inner Solar System then - on Earth this coincides with the Cambrian Explosion, when life on Earth started evolving more rapidly.
The h2g2 Tour of the Solar System
Take the h2g2 Shuttle for your whistle-stop tour of the Solar System.