The Oort comet theory proposed in 1950 has been extended and modified by modern research. Creationists have used short-period comets as a young-age indicator and suggested that comets caused impacts on the moon and the earth. The original ideas of Jan Oort from 1950 have been modified by scientists today to deal with difficulties in Oort’s original proposals. This paper reviews modern theories on comets, especially regarding the orbital dynamics of the different types of comets. Short-period comets are considered as two separate groups: the Jupiter-family comets and the Halley-type comets. Both groups of short-period comets have a limited "lifetime." Long-period comets and near-parabolic comets also are considered as the original rationale for the Oort theory. A young-age view suggests that long-period and near-parabolic comets may have been created along their current orbits, headed inbound toward the sun. Naturalistic comet theories have experienced difficulties related to explaining how comets could make the necessary transitions from one type of orbit to another. The Oort theory is also believed to apply to extrasolar planetary systems. This implies that it should be possible to observe interstellar extrasolar comets, yet none have been observed. These issues show that though it is widely accepted by astronomers, the Oort comet theory has not been successful.