Acoustic metamaterials (AMs) are artificially structured materials composed of subwavelength units that enable acoustic phenomena not achievable with conventional materials and structures. This review defines and presents a distinct category referred to as soft acoustic metamaterials (SAMs), which use soft materials or reconfigurable structures to achieve enhanced acoustic functionality. These systems make use of the inherent flexibility of their materials or the deformability of their geometry to support passive, active, and adaptive functions. To capture this structural and functional diversity, we introduce a three-dimensional classification that considers geometry, acoustic control mechanisms, and functional responsiveness as interrelated aspects. The geometry is classified into two-dimensional metasurfaces and three-dimensional bulk structures. The control mechanisms include local resonance, phase modulation, attenuation, and structural reconfiguration. The response type refers to whether the system behaves passively, actively, or adaptively. Using this approach, we provide an overview of representative implementations and compare different design approaches to highlight their working principles and application areas. This review presents a structured classification for soft acoustic metamaterials and offers a foundation for future research, with broad potential in intelligent sound systems, wearable acoustics, and architectural applications.