Modularity concepts have been recently explored in the context of industrial production (manufacturing) systems such as chemical processes, energy systems, and infrastructures. Standardization and size reduction brought by modular technologies enable mass off-site fabrication, fast transportation, and deployment of equipment, which could ultimately lead to technology cost reductions. Modular systems, contrasting with large and centralized systems that involve lengthy on-site construction phases and difficult transportation (and are thus rarely relocated), also enable sequential investment strategies that provideflexibility to mitigate market and regulatory risks. Therefore, a thorough study of modularity concepts using computational frameworks and optimization tools is required. We study modularity in the context of manufacturing systems and address the following three questions: what is modularity (concepts), why should we consider modular designs (benefits), and how can we incorporate modular concepts in actual designs (usage). Specifically, we first propose a modularity measure that captures unique characteristics in the context of manufacturing systems. Then, we study the spatial and temporal flexibility brought by modular construction (decentralization in electricity market and capacity expansion planning). Finally, we propose a system-level design concept: spatial superstructure, and based on this new concept, we derive a formulation that provides optimal spatial modular design of a process or supply chain. By providing a complete story on modularity in manufacturing and supply chain, we seek to encourage incorporating modular concepts in future process and supply chain designs. In this work, we provide necessary definitions and computational frameworks that aid the modular process design and solve potential design problems such as scalability.