This article by Marc Fleurbaey and Stephan Klasen features in the World Social Science Report 2016. This contribution analyses the future evolutions of inequality and social progress. World inequalities have evolved in a complex way over the past few decades. The economic emergence of several developing countries with large populations has lowered global inequality, while the widening of inequalities within countries has served to increase it. Many future evolutions are possible. The baseline scenario would see the world go back to a nineteenth-century pattern of large social inequalities. Less unequal scenarios could involve political intervention to reduce inequalities domestically, or quicker convergence between countries. In all scenarios, the convergence of living standards will raise serious environmental challenges.