The value chain, as an analytical tool, has been used for more than 50 years as a way to better understand how agri-food products move and gain value from the farm gate to the table. Over the past 20 years, increasing attention has been paid to questions of sustainability within value chains and even more recently there has been a push to try to better understand how the way through which food is provisioned can deliver diets that are also sustainable. In this chapter, we explore the recent advances in value chain theories and we illustrate how taking a horizontal network, systemic and territorialized approach to food provisioning systems contributes to this literature. We argue that by looking both within and across value chains, we can better identify innovations in actor arrangements that are bringing new values (particularly sustainability) into food systems. By refocusing our analytical lens away from specific commodities and towards new forms of organization - such as short supply chains, circular economies, gastronomy and geographical indications - we can better capture how they might contribute to promoting sustainable consumption and production in local food systems.