Nowadays, around 690 million undernourished people worldwide, even though the world already produces enough food to feed more than the whole current population. This situation is far from diminishing due to the current COVID-19 worldwide health contingency and other environmental threats, e.g., climate change. This work establishes key parameters to build a sustainable agri-food system that allows characterizing the degree of sustainability of the global agri-food system following the food sovereignty framework. It is divided into three main sections, two of them has a published article. The first one proposes a quantitative methodology that analyzes food systems' functioning at the international level. That section presents a database with 97 indicators distributed into six categories: 1) access to resources; 2) productive models; 3) commercialization; 4) food consumption and the right to food; 5) agrarian policies and civil society organization, and 6) gender. Then, the second section advances the concept of food sovereignty as a conceptual framework to analyze agri-food systems' sustainability following the steps proposed by Jabareen (2009) to build conceptual frameworks. The third section presents a quantitative multivariate assessment of 43 indicators of food sovereignty and 39 indicators of socio-demographic and social well-being and environmental sustainability in 150 countries. Finally, I conclude this dissertation with final remarks and further work on the forthcoming final paper submitted in the first quarter of 2021.