For functional or aesthetic reasons, many a structural system is designed to be spatially periodic; namely, it is composed of identical sub-units which are connected to form a spatially periodic pattern. The main construction of the hull of a ship, the fuselage of an aircraft, and a space antenna are examples. Such a structure possesses interesting dynamic properties. However, due to material, geometric and manufacturing variabilities, an ideally periodic structure does not exist. The departure from the ideal designed configuration is known as disorder, which can cause drastic change in the dynamic behavior. The present paper gives a review of some recent works on wave propagation and frequency response of disordered periodic structures, of interest to researchers on vibration and noise control.