In this paper, a general ray-theoretical representation of the X-wave pulse is introduced. This representation is based on pulsed plane waves having wave vectors lying on a conic surface. The pulsed plane wave representation is used to study the behavior of X-waves in the presence of planarly layered media. In the case of an interface separating two semi-infinite media, the pulsed plane wave representation provides a clear explanation for the disintegration of the transmitted field. It shows that unlike the incident and reflected fields, the wave vectors associated with the transmitted field do not lie on a cone. Furthermore, this approach allows one to estimate several characteristic properties of the layered media (e.g., dielectric constant and thickness of each layer) from the time of arrival of the reflected X-waves.