We study a class of acoustic metamaterials formed by layers of perforated plates and producing negative refraction and backward propagation of sound. A slab of such material is shown to act as a perfect acoustic lens, yielding images with subwavelength resolution over large distances. Our study constitutes a nontrivial extension of similar concepts from optics to acoustics, capable of sustaining negative refraction over extended angular ranges, with potential application to enhanced imaging for medical and detection purposes, acoustofluidics, and sonochemistry. DOI: 10.1103/PhysRevLett.108.124301 PACS numbers: 43.35.+d, 42.79.Dj, 81.05.Xj Optical negative refraction is a counterintuitive phenomenon that consists in bending light the wrong way at the interface between suitably engineered materials. Homogeneous substances with refraction indices of opposite signs provide an ideal combination on which this effect can take place. Over four decades ago, Veselago [1] realized that a material with simultaneous negative magnetic permeability and electric permittivity must have negative index and, therefore, can produce negative refraction. Subsequently, Pendry [2] showed that a slab of such material can amplify evanescent fields, from which a perfect lens can be constructed, capable of yielding images with deep subwavelength resolution. These concepts have been realized in artificial metamaterials, textured on a small scale compared to the wavelength and displaying homogeneous resonant electric and magnetic response [3,4].Inspired by these exotic optical phenomena, the quest for acoustic superlensing and negative refraction started with the prediction of negative index of refraction in materials exhibiting negative effective mass density and negative bulk modulus at the operating frequency [5]. In this context, several acoustic metamaterial designs have been proposed containing resonators in the form of coated metallic spheres [6], lumped elements [7], or perforations [8]. However, isotropic acoustic negative-index materials have not been experimentally realized to date, despite a long tradition of sound control using resonant linear devices [9,10], including applications to diffraction-limited imaging [11]. An alternative approach to acoustic negative refraction and lensing is suggested by electromagnetic metamaterials relying on anisotropy [12].In this Letter, we show that a holey anisotropic metamaterial can exert subwavelength control over sound waves beyond what is achieved with naturally occurring materials. We predict that, for appropriate choices of geometrical parameters, these metamaterials support negative refraction, backward-wave propagation along a direction opposite with respect to the acoustic energy flow, and subwavelength imaging with both the source and the image situated many wavelengths away from the material. Acoustic subwavelength control can be advantageous for (bio)medical ultrasonography and diagnostic imaging [13], acoustofluidic steering of microparticles and microorganisms [14], and sono...