The environmental crisis is forcing societies to rethink how they operate and manage resources. In this context, circularity frameworks have emerged, underpinned by intentions to close the loops of material and energy cycles in order to improve the environmental and socioeconomic performance of anthropic systems. In this article, we combine five contrasting case studies focusing on material flows within different components of the agri-food system: assessment of livestock farming; material flow representations for a territorial development strategy; evaluation of food waste flow and loss; analysis of potential pollution of urban green space lands; and governance of methanization projects. The results illustrate the value of quantitative analyses of material flows and studies of the governance of these flows to support local territorial development strategies. They also highlight the limits of these analyses and the blind spots, especially the difficulty of reproducing the complexity of interactions, the limits of the analogy between natural biological cycles and recycling loops, in particular with respect to environmental and sanitary considerations, and the limited effective contribution of these analyses to the emergence of territorial innovations, beyond raising local actors' awareness of the material dimension and environmental impacts of their activities. The toolset offered by circularity frameworks is relevant by their multi-criteria and multidisciplinary characteristics, but it still largely remains to be integrated. The articulation between quantitative analyzes of material and energy flows and the governance mechanisms largely remains to be invented in order to think about and implement sustainable transition in the territories.