Initially proposed to achieve strong noise isolation levels beyond the mass-density law, acoustic metamaterials (AMMs) have now overturned the conventional views in all aspects of sound propagation and manipulation. In fact, within the last two decades, these artificial materials have enabled improved control over the propagation of sound waves by allowing one to engineer macroscopic effective properties well beyond what is naturally available. In this review, we first trace the development of passive AMMs from their initial realizations based on locally resonant structures to their more advanced versions, like space-coiling, holey and labyrinthine metamaterials, Willis materials, and subwavelength crystalline metamaterials, highlighting their basic working principles and applications. We then survey more recent research topics, including non-Hermitian, non-reciprocal, and topological acoustic metamaterials. Altogether, this paper provides a comprehensive overview of research on acoustic metamaterials, and highlights prominent future directions in the field, including topological and active metamaterials.