This study explains the business model innovation processes in industrial firms. Drawing on three case studies of leading business-to-business firms shifting from product-based to service-based business models, it introduces problems as a theoretical concept to explain business model innovation processes. We show how formulating and solving problems guide the search for a viable business model and why some problem formulation and solving activities lead firms to shift between backward-looking and forward-looking searches. The decision to shift to a forward-looking search is triggered by the perception of failure to continue with an established way of working, while the shift to a backward-looking search is based on the perception of high alternative costs. We contribute to the business model innovation and servitization literature by theorizing the process of business model innovation and providing implications for managers. © 2022 The Authors