The effective control of lowfrequency vibration and noise has always been a classic challenge in the field of dynamics and control, and there is an urgent need for new ideas for cross research. As an important branch of dynamics and control, the research on acoustic metamaterials and crystal growth has been highly valued in recent years. With the support of the national science and technology department and related industries, significant progress has been made in the study of vibration and noise control mechanisms and applications of acoustic metamaterials and phononic crystals. This article starts from the research perspectives of the development trends and application prospects of acoustic metamaterials and phononic crystals, focusing on the design methods and vibration and noise reduction characteristics of acoustic metamaterials, the impact and energy absorption characteristics of mechanical metamaterials, and the methods of sound field suspension and transportation. These achievements to some extent reflect the current concerns and proposed solutions of the authors, hoping to provide some reference and reference for other researchers in acoustic metamaterials and phononic crystals.