Max Mathews is well known as the ‘‘Father of Computer Music,’’ having written the first program for generating digital sound samples from high‐level ‘‘note’’ and ‘‘instrument’’ specifications. Instruments were specified as interconnections of elemental building blocks called unitgenerators. This presentation reviews some of the history and impact of the unit‐generator concept in computer music over the past half‐century. Widespread dissemination of the unit‐generator architecture for sound synthesis began with the Music V Program (the first Fortran version), written by Max Mathews in 1968. Derivatives soon appeared at research universities, such as csound (Vercoe, MIT), Mus10 (Chowning’s group, Stanford), and cmusic (Moore, UCSD). Hardware acceleration for unit generators appeared in the 1980s. Later, Music‐V descendants included Lisp‐based music compilers such as Common Lisp Music (CLM), the Synthesis Tool Kit in C++ (Cook etal., Princeton), and graphical programming languages for real‐time music processing/synthesis, such as Max/MSP and Pure Data (PD) started by Miller Puckette. More recent descendants include SuperCollider (McCartney, UCSB) and ChucK (Wang etal., Princeton). Thus, the unit‐generator architecture, introduced by Max Mathews half a century ago, has firmly taken root as a preferred modular approach to the problem of constructing virtual musical instruments and digital audio effects.