We explore the largely uncharted scattering properties of acoustic systems that are engineered to be invariant under a special kind of space-time symmetry, consisting in taking their mirror image and running time backwards. Known as Parity-Time symmetry, this special condition is shown here to lead to acoustic metamaterials that possess a balanced distribution of gain (amplifying) and loss (absorbing) media, at the basis of ideal loss-compensation, and under certain conditions, unidirectional invisibility. We have designed and built the first acoustic metamaterial with parity-time symmetric properties, obtained by pairing the acoustic equivalent of a lasing system with a coherent perfect acoustic absorber, implemented using electro-acoustic resonators loaded with non-Foster electrical circuits. The active system can be engineered to be fully stable and, in principle, broadband. We discuss the underlying physics and present the realization of a unidirectional invisible acoustic sensor with unique sensing properties. We also discuss the potential of PT acoustic metamaterials and metasurfaces for a variety of metamaterial-related applications, which we obtain in a loss-immune and broadband fashion, including perfect cloaking of sensors, planar focusing, and unidirectional cloaking of large objects.