Analytical modeling plays an important role in evaluating computer system performance during the design, development and configuration of a system. We will survey analytical computer performance modeling with an emphasis on developments of practical importance. In doing so the symbiotic relationship between computer performance modeling and queueing theory, in particular queueing networks, will be made evident. The survey will proceed historically, starting with developments in the mid-1960s, when the first published results on queueing models of multiprogramming and time sharing systems appeared, and continuing to include current areas of research. The computer systems we will consider include conventional single processor systems as well as highly parallel multiprocessor systems. Both subsystem models and overall system models will be discussed. It is intended that in addition to being of interest to the computer science community this paper will expose queueing theorists and applied queueing analysts to the practical queueing analysis problems that arise in computer performance modeling. © 1989.