From the 1980s onward, income inequality increased in many advanced countries. It is very difficult to account for the rise in income inequality using the standard labour supply/demand explanation. Fiscal redistribution has become less effective in compensating increasing inequalities since the 1990s. Some of the basic features of redistribution can be explained through the optimal tax framework developed by J. A. Mirrlees in 1971. This Element surveys some of the earlier results in linear and nonlinear taxation and produces some new numerical results. Given the key role of capital income in the overall income inequality, it also considers the optimal taxation of capital income. It examines empirically the relationship between the extent of redistribution and the components of the Mirrlees framework. The redistributive role of factors such as publicly provided private goods, public employment, endogenous wages in the overlapping generations model and income uncertainty are analysed.