Sustainability is a complex concept that deals with different dimensions which are economic, social, environmental, cultural and governance-related. Therefore, the aim of a sustainable production should take into consideration all the inputs (natural and social resources) and a particular attention should be given at their protection in order to let them be reproducible in the long-run. In Geographical Indication (GI) products the aim of developing sustainable food production is evident and tangible. In these products not only the value chain dimension is important, but especially the territorial one. The latter, oft described through the French concept of terroir, strictly relates the product to the producers thanks to the raw materials (for their specific attributes gained due to the geophysical characters) and the know-how (for the attributes, which arise as a consequence of the tradition and the human elements). The objective of the paper is to describe in a comprehensive way a theoretical framework, which includes the variables that affect the sustainability, starting from the Sustainability Assessment of Food and Agriculture Systems (SAFA) method proposed by the Food and Agriculture Organization of the United Nations (FAO), aggregating together the distinct dimensions (environmental, economic, social and governance-related). The method described is the one applied at a European Project: Strength to Food, focusing on a specific case-study: the Parmigiano Reggiano cheese. The results and the suggestions derived from the observations made on this specific case-study.