The future livestock systems at the world level will have to produce more in the perspective of the population increase in the next 30 years, whereas reducing their environmental footprint and addressing societal concerns. In that perspective, we may wonder if animal health and animal welfare, which are two essential components of production systems, may play an important role in the stability of the three pillars of sustainability of the livestock systems. We already know that objectives driven by economy, environment and society may modify animal welfare and animal health, but is the reverse true? The answer is yes and in 11 cases out of 12 of the matrix health-welfare×3 pillars of sustainability×positive or negative change, we have many examples indicating that animal health and animal welfare are able to modify, positively or negatively, the three pillars of sustainability. Moreover, we also have good examples of strong interactions between health and welfare. These elements play in favour of an holistic approach at the farm level and of a multicriterial definition of what could be the sustainable systems of animal production in the future which will respect animal welfare and maintain a good animal health.