Classification is an important activity that facilitates theory development in many academic disciplines. Scholars in fields such as organizational science, management science and economics and have long recognized that classification offers an approach for ordering and understanding the diversity of organizational taxa (groups of one or more similar organizational entities). However, even the most prominent organizational classifications have limited utility, as they tend to be shaped by a specific research bias, inadequate units of analysis and a standard neoclassical economic view that does not naturally accommodate the disequilibrium dynamics of modern competition. The result is a relatively large number of individual and unconnected organizational classifications, which tend to ignore the processes of change responsible for organizational diversity. Collectively they fail to provide any sort of universal system for ordering, compiling and presenting knowledge on organizational diversity. This paper has two purposes. First, it reviews the general status of the major theoretical approaches to biological and organizational classification and compares the methods and resulting classifications derived from each approach. Definitions of key terms and a discussion on the three principal schools of biological classification (evolutionary systematics, phenetics and cladistics) are included in this review. Second, this paper aims to encourage critical thinking and debate about the use of the cladistic classification approach for inferring and representing the historical relationships underpinning organizational diversity. This involves examining the feasibility of applying the logic of common ancestry to populations of organizations. Consequently, this paper is exploratory and preparatory in style, with illustrations and assertions concerning the study and classification of organizational diversity.