Abstract: Periodic structures find many practical applicationsin engineering. They have special dynamiccharacters such as frequency passbands and stopbands. Disorder canresult in radical changes of their mechanical properties.In disordered periodic structures, one may see vibration localization.Localization destroys the regularities of vibration modes ofperiodic structures and some parts of the structures may have very largevibration amplitudes under external excitations. This may lead to energyaccumulation oreven destroy the structures. So it is very important to analyze thepropagation characteristics of vibration and energy in disordered periodicstructures, which can provide theoretical bases for the vibration controland vibration reduction of substructures. This paperreviews the current development of the investigations on the vibrationlocalization in one-dimensional linear periodic structures, cyclic periodicand two-dimensional periodic structures. The discussion is focused on theestablishment of mechanical models, analytical methods and other issuesin vibration localization. Finally,some problems for further studies are suggested.