Abstract: Metamaterial, a type of burgeoning man-made material/structure, possesses a periodic/quasi-periodic structure and is able to change the transmission properties of the electromagnetic wave, the acoustic wave and the elastic wave. Due to its enormous potentiality in the field of the spaceflight, national defence and civilian, the metamaterial attracted great interest, inspired a new wave of research and obtained consecutive important achievement since it was proposed. Elastic wave metamaterial is a kind of metamaterial which is capable of realizing the attenuation and manipulation of the elastic wave on the basis of the interaction of the elastic wave and the periodic/ quasi-periodic structure. Band structure design is an important tool for the elastic wave metamaterial to execute the wave manipulation and attenuation. The location, width and wave suppression performance of the frequency band are related to the nature of materials, the lattice constant of the metamaterial, and the resonant frequency of the local resonator. Because of the limitations such as the carrying capacity, the overall size, and the structure of the local resonator, it is still difficult to obtain an elastic wave band gap in the frequency range around 100 Hz through the conventional metamaterials. This review introduces the fundamental principle of the metamaterial for opening elastic wave band gaps firstly, and then elaborates the low-frequency elastic wave metamaterial from three aspects: the fundamental configuration of the metamaterial, the low-frequency band gap optimization and tuning, and some potential applications. The fundamental configurations of low-frequency elastic wave metamaterials mainly include three aspects: Bragg scattering metamaterials, conventional local resonant metamaterials and quasi-zero-stiffness local resonant metamaterials. The low-frequency band tunability achieved by both the passive and active approaches detailed as well. This review summarizes the current knowledge of the low-frequency elastic wave metamaterial, analyzes the inadequacies and the advantages in current research, and outlines future research prospects.