This article by Marcelo Medeiros features in the World Social Science Report 2016. Inequality in Brazil fluctuates over time, but has been high since at least 1928, as a result of an impressive concentration of income among the rich. This contribution analyses the viability of commonly proposed strategies to reduce inequality. It argues that a realistic expansion of education, the eradication of poverty, the expansion of social assistance programmes, economic growth and a more efficient management of current policies will not have major impacts on inequality within a reasonable time frame of, say, two decades.