Servitization and Industry 4.0 are considered two of the most recent trends transforming industrial companies. Servitization is mainly focused on adding value to the customer (demand-pull) while Industry 4.0 is frequently related to adding value to manufacturing process (technology-push). Although some scholars address them as complementary concepts, the literature lacks evidences about what are the interfaces and connection between the two trends. Thus, we aim to develop a conceptual framework that connects Servitization and Industry 4.0 concepts from a business model innovation (BMI) perspective. Our framework is based on three Servitization levels (i.e. smoothing, adapting and substituting) and three levels of digitization (i.e. low, moderate and high levels). We show that matching these levels results in nine possible configurations classified in manual, digital and industry 4.0-related services, which can focus on smoothing, adapting or substituting services. We use reported cases from the literature to support and illustrate these configurations. We also discuss different levels of complexity for the implementation of these configurations. The study hence provides a foundation for the growing research on the interface between Servitization and Industry 4.0.