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Acoustic metamaterials are engineered materials that were extensively investigated over the last years mainly because they promise properties otherwise hard or impossible to find in nature. Consequently, they open the door for improved or completely new applications (e.g. acoustic superlens that can exceed the diffraction limit in imaging or acoustic absorbing panels with higher transmission loss and smaller thickness than regular absorbers). Our objective is to surpass the limited frequencyoperating range imposed by the resonant mechanism that s1ome of these materials have. In addition, we want acoustic metamaterials that could be experimentally demonstrated and used to build devices with overall performances better than the previous ones reported in the literature.Here, we start by focusing on the need of engineered metamaterials in general and acoustic metamaterials in particular. Also, the similarities between electromagnetic metamaterials and acoustic metamaterials and possible ways to realize broadband acoustic metamaterials are briefly discussed. Then, we present the experimental realizationand characterization of a two-dimensional (2D) broadband acoustic metamaterial with strongly anisotropic effective mass density. We use this metamaterial to realize a 2D broadband gradient index acoustic lens in air. Furthermore, we optimize the lens design by improving each unit cell's performance and we also realize a 2D acoustic ground cloak in air. In addition, we explore the performance of some novel applications (a 2D acoustic black hole and a three-dimensional acoustic cloak) using the currently available acoustic metamaterials. In order to overcome the limitations of our designs, we approach the active acoustic metamaterials path, which offers a broader range for the material parameters values and a better control over them. We propose two structures which contain a sensing element (microphone) and an acoustic driver (piezoelectric membrane or speaker). The material properties are controlled by tuning the response of the unit cell to the incident wave. Several samples with interesting effective mass density and bulk modulus are presented. We conclude by suggesting few natural directions that could be followed for the future research based on the theoretical and experimental results presented in this work.