An overview of the unique computational requirements and continuing challenges for the numerical simulation of acoustic signals is presented.  Proper resolution and propagation of an acoustic signal necessitates numerical techniques that are essentially free of dispersion and dissipation, thus ruling out tradition formulations used in computational fluid dynamics.  A brief survey of high-order techniques coupled with a detailed look at the resolution characteristics of implicit finite difference operators will be shown.  Particular attention will be given to the implementation of non-reflecting boundary conditions (including those adapted from computational electromagnetics) as well as a discussion of results from the recent NASA workshop on benchmark problems in computational aeroacoustics.