It is now well understood how coordinate transformations of the Maxwell equations can be interpreted in terms of an electromagnetic material in the original coordinates with transformed values of permittivity and permeability. Through this transformation optics approach, the bending and stretching of electromagnetic fields specified by coordinate transformations can be implemented with electromagnetic materials, enabling unexpected and interesting solutions such as electromagnetic cloaking. In this presentation we describe work by us and others that show how this same concept can be extended to realize arbitrary manipulations of acoustic waves, including cloaking, using materials with very specific properties. While the concept of transformation acoustics was first demonstrated by analogy with electromagnetics, here we derive it from first principles through an analysis of the divergence and gradient operators under coordinate transformations. We will also discuss several approaches for engineering composite materials with the acoustic properties needed to realize transformation acoustics devices and demonstrate their performance through full wave simulations.