Abstract: Phononic crystals are a novel type of acoustic functional material proposed in the early 1990′s. This kind of periodically elastic structure exhibits many important properties, such as phononic bandgaps, in which the propagation of vibration and sound are forbidden. The position of the bandgaps and passbands can be engineered by calculating the acoustic wave equations of the crystals. The existence of these bandgaps is closely associated with the Anderson localization of phonons in inhomogeneous media. The main features, theoretical methods used to study them, potential applications and future prospects are discussed.