In this paper, we study how the tax-and-transfer system reduces the inequality of lifetime income by redistributing lifetime earnings between individuals with different skill endowments and by providing individuals with insurance against lifetime earnings risk. Based on a dynamic life-cycle model, we find that redistribution through the tax-and -transfer system offsets around half of the inequality in lifetime earnings that is due to differences in skill endowments. At the same time, taxes and transfers mitigate around 60% of the inequality in lifetime earnings that is attributable to employment and health risk. Progressive taxation of annual earnings provides little insurance against lifetime earnings risk. The lifetime insurance effects of taxation may be improved by moving to a progressive tax on lifetime earnings. Similarly, the lifetime insurance and redistributive effects of social assistance may be improved by requiring wealthy individuals to repay any social assistance received when younger.