The concept of modularity has gained considerable traction in technology studies as a way to conceive, describe and innovate complex systems, such as product design or organizational structures. In the recent literature, technological modularity has often been intertwined with business model innovation, and scholarship has started investigating how modularity in technology affects changes in business models, both at the cognitive and activity system levels. Yet we still lack a theoretical definition of what modularity is in the business model domain. Business model innovation also encompasses different possibilities of modeling businesses, which are not clearly understood nor classified. We ask when, how and if modularity theory can be extended to business models in order to enable effective and efficient modeling. We distinguish theoretically between modularity for technology and for business models, and investigate the key processes of modularization and manipulation. We introduce the basic operations of business modeling via modular operators adapted from the technological modularity domain, using iconic examples to develop an analogical reasoning between modularity in technology and in business models. Finally, we discuss opportunities for using modularity theory to foster the understanding of business models and modeling, and develop a challenging research agenda for future investigations.