Phononic crystal is a novel type of acoustic functional material,study of which has aroused great attention of people all over the world.The researches on phononic crystal are reviewed and the questions on research of phononic crystal analyzed.Also some concepto,the property and the basic calculating method are discussed.It is emphasized that the propagation of the elastic wave in medium with periodic structure may be controlled by the existence of the gap and defect.The prospect of the research on phononic crystal is discussed as well.