The concept of food system has gained prominence in recent years amongst both scholars and policy-makers. Experts from diverse disciplines and backgrounds have in particular discussed the nature and origin of the “unsustainability” of our modern food systems. These efforts tend, however, to be framed within distinctive disciplinary narratives. In this paper we propose to explore these narratives and to shed light on the explicit -or implicit- epistemological assumptions, mental models, and disciplinary paradigms that underpin those. The analysis indicates that different views and interpretations prevail amongst experts about the nature of the “crisis”, and consequently about the research and priorities needed to “fix” the problem. We then explore how sustainability is included in these different narratives and the link to the question of healthy diets. The analysis reveals that the concept of sustainability, although widely used by all the different communities of practice, remains poorly defined, and applied in different ways and usually based on a relatively narrow interpretation. In so doing we argue that current attempts to equate or subsume healthy diets within sustainability in the context of food system may be misleading and need to be challenged. We stress that trade-offs between different dimensions of food system sustainability are unavoidable and need to be navigated in an explicit manner when developing or implementing sustainable food system initiatives. Building on this overall analysis, a framework structured around several entry points including outcomes, core activities, trade-offs and feedbacks is then proposed, which allows to identify key elements necessary to support the transition toward sustainable food systems.