In the final decades of the twentieth century, experts in a wide variety of disciplines—such as computer science, evolutionary biology, management studies, and educational theory—introduced the concepts of modular design into their professional discourses and practices. In each of these disciplines, modular systems called for standardized, interchangeable components (or modules) that could be recombined within a predefined system architecture. This article explores the modern history of modularity as it was imagined and applied in two specific settings: the architectural theories of Albert Farwell Bemis in the 1930s and the construction of electronic computers in the 1950s and 1960s. By framing this account as a history of an ordering concept, I hope to persuade information historians to look across traditional disciplinary boundaries and examine the more general set of concepts, strategies, organizations, and technologies that humans have used in their unending efforts to order and make sense of information.