They can loose their tail or develop multiple tails or break apart and fall into the sun. Sometimes they can even split into two or more pieces, so that, through a telescope, several comets can be seen moving together across the sky. Once brought into the inner solar system, comets life span shorten greatly. After just a few orbits about the sun, the ice is melted away and all that remains is stellar dust or rock. Comets are also cause many of earth's well known meteor showers.
Comets travel in elliptical orbits and their tail usually points away from the sun.
From Tycho's observations, Kepler was able to deduce his now famous laws of motion which help explain the motion of comets and any other object that orbits. In 1994, the comet Shoemaker-Levy impacted Jupiter. Before striking Jupiter, the comet fragmented into several large chunks. Comet Shoemaker -Levy streaming toward Jupiter.