Organizations continually realise that fulfilling their sustainability objectives requires emerging innovations and innovation in the business model. Initially, most research revolved around product or method innovations with a new field of concern for the innovation in the business for its sustainability. A variety of new techniques & strategies have been designed to promote sustainability in the business models. While creating a large variety of business models, very few have been introduced successfully. Despite the topic's importance, research shows that many business model innovations fail. The causes of failure are largely unexplored and there is a lack of a comprehensive review of the literature on innovation in sustainable business models. The identified gaps in the areas of sustainable business model innovation that undermine bridging the design-implementation gaps are; the process of implementing business model innovation; its tools; and its challenges. The Cambridge Business Model innovation process (CBMIP) enables current and newly designed tools to be incorporated into the market modelling process, showing deficiencies.