Throughout the world, livestock grazing systems (LGS) include and provide livelihoods for many rural populations. These LGS are represented in a wide variety of agroecological contexts and offer a huge variety of system organization. They contribute to sustainable food systems by providing multiple products including low-cost edible proteins and energy, draft power, outputs (carbon and soil nutrient regulation, landscape and biodiversity maintenance), roles (local development support in harsh environments, contribution to the circular economy) and benefits to population (revenue, employment and cultural assets). These multiple functions can be described through a multifunctional conceptual model specified for LGS. Applied to cases in Africa, Asia, Latin America and Europe, the framework enables the assessment of these systems in a holistic manner that includes four dimensions: production, social, environmental and local development. These dimensions and associated local indicators demonstrate the potential important contribution LSG makes to sustainable food systems. Management of trade-offs between these functions may be improved using, such a model in a multi-stakeholder approach. Some of the functions and balance between them might have been overlooked in the consideration of European food systems.