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Most comets revolve around the sun in flat elliptical orbits. This kind of comet is called "periodic comet". Every once in a while, we will have the opportunity to see it in the orbit closer to the sun and the earth. Comets have different periods around the sun. The shortest one is called "Comet Cohen" with a period of 3.3 years. Since the discovery of 1786, it has appeared more than 60 times. Some comets have a long period, and they can only be seen once in decades or even hundreds of years.
Some comets have a period of tens of thousands of years or even longer. These comets are like passers-by. Once they leave, they don't know where to go.
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We can only see comets with elliptical orbits, that is, periodic comets, and then we can't see parabolic and hyperbolic orbits.