A vibration-based monitoring process is proposed that adopts a different viewpoint than modal-based methods currently practiced. In addition to the usual modal characterization, vibrations can also be described as traveling waves, which propagate in a continuous structure and are reflected and transmitted at a structural discontinuity. While modal responses depend on the global properties of the structure, the reflection and transmission characteristics depend only on the local properties of the structural damage. As a result, structural health monitoring based on wave vibration characteristics is more sensitive and reliable. In this paper, the wave based vibration approach is applied in monitoring both a cracked structural element and a cracked structural joint. Numerical examples are presented.