Purpose: To make their supply chains more socially responsible, many companies are implementing supplier assessment tools and collaborative practices. The aim of this paper is to provide a systematic literature review on the governance structures used to extend sustainability to suppliers. More specifically, the authors aim to answer two questions: "What is the impact of these mechanisms or governance structures on sustainable performance?" and "What are the enablers of these mechanisms?". Design/methodology/approach: A structured literature review is carried out that analyses published studies, evaluates contributions, summarises knowledge and identifies managerial implications and lines for further research. Findings: Both assessment and collaboration have a positive impact on environmental performance and corporate social responsibility, although the most recent collaborative paradigm stresses that assessment alone is not enough. Some enablers of these practices are identified. Research limitations/implications: Although the authors believe that the right search terms have been used, the choice of these terms could be a limitation of this study. Also, the selection of the articles could be considered subjective, although the papers were reviewed by two researchers. Practical implications: Supplier assessment and collaboration are effective in improving sustainability. However, the results also indicate that assessment alone is not enough. Firms also need to adopt a collaborative approach. Finally, a list of enablers to implement these practices is provided. Originality/value: The paper summarises knowledge related to the impact of supplier assessment and collaboration on sustainability, and describes the enablers of such initiatives, providing some managerial implications and lines for further research.