In recent decades, noise pollution has emerged as one of the most significant environmental and public health challenges in urban, industrial, and transportation environments, creating an urgent demand for lightweight, thin, and multifunctional sound-absorbing materials. Textiles, porous foams, and fibrous aerogels have attracted considerable attention as promising noise-control platforms due to their low weight, flexibility, and ease of integration into various structures. However, their acoustic performance is often limited, particularly at low frequencies and under thickness constraints. In this context, metal–organic frameworks (MOFs), characterized by exceptionally high specific surface area, tunable porosity, low density, and tailorable surface chemistry, have emerged as highly promising candidates for enhancing the acoustic properties of these materials. This review provides a comprehensive and analytical assessment of the role of MOFs in improving the acoustic performance of polymeric foams, textiles, and fibrous aerogels. The influence of MOF type, pore architecture, substrate characteristics, and fabrication/attachment methods on sound absorption behavior is comparatively discussed. The reviewed studies demonstrate that MOF families such as ZIF, UiO, MIL, HKUST-1, and FeBTC can significantly enhance acoustic performance through the formation of hierarchical macro–meso–micro porous structures, increased tortuosity, optimized airflow resistivity, enhanced viscous–thermal dissipation, localized resonances, and improved acoustic impedance matching. Among the investigated substrates, MOF-based aerogels exhibit the greatest potential for broadband sound absorption due to their multiscale porous networks and outstanding performance-to-weight ratio, whereas MOF-modified textiles and foams offer important advantages in terms of flexibility, durability, and industrial applicability.The review further reveals that although MOFs can substantially improve sound absorption at medium and high frequencies, efficient low-frequency sound attenuation remains a major challenge. The development of gradient architectures, multilayer systems, and MOF-based acoustic metamaterials is therefore highlighted as a promising strategy for overcoming this limitation. In addition, key challenges including mechanical and moisture stability, adhesion to substrates, synthesis cost, scalability of production, and the lack of standardized acoustic evaluation protocols are critically discussed. Finally, future research directions are outlined, emphasizing multiscale hybrid architectures, multifunctional smart acoustic textiles, green synthesis routes, and the integration of data-driven design and machine learning approaches for the development of next-generation acoustic materials.