The way a wave behaves, while propagating across a medium, varies with the wave type and the medium. So, knowledge of the behaviour of a wave in a system with a different form of damage, and behaviour of different types of waves in a particular system is an essential prerequisite for almost all activities in structural system identification and mainly for damage detection and localization of damage. This paper presents a comparative study of various wave propagations, that has been done by researchers in various structural systems. Further, a numerical model of an isotropic plate using finite element is created both with and without damage. The behaviour of waves has been studied. Finally, the comparative result is shown. This paper offers a new perspective for ongoing research by providing the most recent developments, difficulties, and prospects of wave propagation behaviours for damage detection and localization in the commonly used structural systems and structural elements. While propagating through different structural systems and components, the most used waves, which are (a) Shear wave, (b) Rayleigh wave, (c) Ultrasonic wave and (d) Lamb wave, have been thoroughly investigated. Along with several difficult problems for future growth, the summarized observations are provided.