This paper reviews the short history, motivation, numerical and theoretical issues, and development of methods for treating a boundary as a reflective/absorptive surface for the time-domain computation of waves in general and acoustic waves in particular. It begins with the extension and implementation of the frequency-domain impedance to a time-domain impedance-equivalent boundary condition (TDIBC), and illustrates how the theoretical, numerical, and implementation issues are addressed and resolved for acoustic/aeroacoustic applications. Comments are also made on the extendibility and applicability of the concept and TDIBC to other fields and types of problems.