Organisations increasingly understand that meeting their sustainability ambitions does not only require new technologies, but innovation on the business model level. To facilitate the design of more sustainable business models, a range of new tools and techniques have been developed. While this resulted in the design of a wide range of promising business models, only very few are successfully implemented. The Cambridge Business Model Innovation Process is a framework developed to guide organisations’ business model innovation efforts and map the necessary activities and potential challenges. In this paper, we introduce the framework and present an exploratory attempt of applying it to a social start-up. The preliminary result of this experience led us to build a comprehensive research agenda that aims at developing tools and processes to help organisations in bridging the design-implementation gap in sustainable business model innovation.