Numerical simulation is an indispensable tool in modern acoustics, and many distinct frameworks have emerged. A use case to be discussed here is the emulation of room acoustics, or so-called virtual acoustics, as well as the related case of realistic sound synthesis based on musical instrument models. In the context of audible sound, particularly when nonlinear mechanisms are present, time-domain methods are commonly used. In this talk we re-examine the use of numerical time-stepping methods with such audio-rate sound output in mind. After a brief overview of such methods, and the presentation of a variety of examples, spanning the full range of virtual acoustics and musical instrument models, attention is turned to practical matters---viewed from the point of view of audio-rate simulation. These include: numerical accuracy, and how this idea aligns with conventional notions such as “order of accuracy” of a given numerical method; methods of ensuring numerical stability for low-loss and possibly strongly nonlinear systems and over long simulation durations; and efficiency, especially for very large problem sizes. Many video and audio demonstrations will be presented.