The orbits of more than 878 comets have been cataloged. Some of the others may be periodic, but their orbits are not understood clearly. Comets have been described as dirty snowballs or icy mudballs. They are mixtures of water ice, frozen gases and dust that for whatever reason didn't get picked up and incorporated into the planets when the Solar System formed. Astronomers think of comets as samples of the earliest history of the Solar System.
Comets are invisible to people on Earth, except when they are near the Sun.
Most fly along highly eccentric orbits, which take them far out beyond the orbit of the most-distant planet, Pluto. They are seen once and then disappear for thosuands of years. After 500 or so trips around the Sun, most of a comet's ice and gas is lost leaving a rocky object very much like an asteroid in appearance. It could be that half of the near-Earth asteroids may be dead comets. Also, a comet whose orbit brings it near the Sun is likely to either hit one of the planets or the Sun, or be thrown out of the Solar System by a close encounter with a major body like Jupiter.