This article begins with a discussion of the general types of porous materials, i.e., rigid, limp, and elastic, and of their general physical properties. The macroscopic properties (e.g., flow resistivity, porosity, tortuosity, etc.) that control the acoustical behavior of each type of porous material are then defined and discussed, as are methods for their measurement. The acoustical characterization of a porous medium is considered next, followed by a discussion of modeling of porous materials with particular reference to elastic porous materials such as foams. The special character of elastic porous materials are illustrated through experimental and computational examples involving sound absorption and sound transmission. In particular, the importance of apparently small details of foam layer boundary conditions is emphasized. Finally, foam finite elements that are capable of predicting the behavior of finite-sized noise control treatments having realistic shapes are discussed. By using foam finite element models it is possible to perform optimal design studies: i.e., to design real treatments that yield optimal acoustical performance at a given treatment volume or weight.