Many detrimental effects on the environment, economy, and society are associated with the structure and practices of food systems around the world. While there is increasing agreement on the need for substantive change in food systems towards sustainability, divergent perspectives exist on what the appropriate points of intervention and strategies to achieve such change are. Change in diets and nutrition, the importance of social food movements, and sustainable farming practices are all disparately featured in the literature; yet, there is little effort to compare and integrate these perspectives. This review offers a comprehensive overview of perspectives on food systems change towards sustainability. We discern where there is convergence and assess how the literature reflects emergent theory on sustainability transformation. We analyzed more than 200 peer-reviewed articles employing an approach that combines quantitative and qualitative analysis. First, we performed a semantic hierarchical cluster analysis of the full texts to identify thematic clusters representing different perspectives on sustainability transformations and transitions of food systems. Second, we conducted a qualitative text analysis for representative articles of each cluster to examine how deep changes in the food system are conceptualized. We identified five distinct approaches to food systems change that are currently discussed, i.e. Alternative food movements, Sustainable diets, Sustainable agriculture, Healthy and diverse societies, and Food as commons. Each approach provides a nuanced perspective on identified sustainability problems, envisioned sustainable food systems, and proposed actions to change food systems towards sustainability. The findings offer guidance for researchers and practitioners working on food systems change towards sustainability.