Acoustic metamaterial science is an emerging field at the frontier of modern acoustics. It provides a prominent platform for acoustic wave control in subwavelength-sized metadevices or metasystems. However, most of the metamaterials can only work in a narrow frequency band once fabricated, which limits the practical application of acoustic metamaterials. This paper highlights some recent progress in tunable acoustic metamaterials based on various modulation techniques. Acoustic metamaterials have been designed to control the attenuation of acoustic waves, invisibility cloaking, and acoustic wavefront engineering, such as focusing via manipulating the acoustic impedance of metamaterials. The reviewed techniques are promising in extending the novel acoustics response into wider frequency bands, in that tunable acoustic metamaterials may be exploited for unusual applications compared to conventional acoustic devices.