The challenges of sustainable development require whole supply chains and networks to drive change and innovation. However, most existing research on sustainable innovations is on a company level and the dominating company focus in practice drives “silo” approaches, short-term thinking, and profit maximization. Consequently, there is a need for research and new models that facilitate sustainable supply chain innovations. The purpose of this paper is to identify, categorize, and evaluate the importance of critical factors for the realization of sustainable supply chain innovation, and to contribute with a process model for the development of sustainable supply chain innovation. A systematic literature review and content analysis of relevant sustainable supply chain innovation literature were performed in five steps starting with (1) question formulation followed by (2) locating studies, (3) selection and evaluation, (4) analysis and synthesis, and (5) reporting and using the results. The analysis resulted in 14 main categories of critical factors. Collaboration is by far the most frequently observed main category, followed by strategic orientation, culture, practices, and political context. The paper contributes with a process model for the realization of sustainable supply chain innovation. The process model is based on a design-thinking model for innovation where the critical factors are integrated into different spaces for innovation. In practice, the model could provide managers with the most critical factors for sustainable supply chain innovation, and could provide advice on when and how to manage these factors during the innovation process. The critical factors and the process model proposed could guide further research, enabling such research to adopt more complex approaches to the development of improved guidance, and provide support for the realization of sustainable development.