Acoustic metamaterials are artificially engineered composites composed of mesoscopic subwavelength units, which have recently become an active field with an enormous range of potential applications. These media, which derive their properties from their structure rather than from the chemical properties of their constitutive materials, can be tailored in such a fashion to exhibit arbitrary effective constitutive parameters, ranging from very large positive to negative values. Initially proposed to achieve super absorption, acoustic metamaterials are today investigated to obtain numerous extraordinary effects, which include compact wavefront modulation, cloaking, asymmetric transmission, subdiffraction focusing, etc. In this article, we review some of the most relevant works in this field and analyse the basic phenomena governing the behaviour of different kinds of acoustic metamaterials. We conclude with an outlook on active acoustic metamaterials, in which inclusions can provide energy to the impinging wave to obtain effective material properties that are not possible in passive structures.