This article reviews recent advances in the study of dynamic taxation, considering three main approaches: the dynamic Mirrlees, the parametric Ramsey, and the sufficient statistics approaches. In the first approach, agents' heterogeneous abilities to earn income are private information and evolve stochastically over time. Dynamic taxes are not restricted ex ante and are set for redistribution and insurance considerations. Capital is taxed only in order to improve incentives to work. Human capital is optimally subsidized if it reduces posttax inequality and risk on balance. The Ramsey approach specifies ex ante restricted tax instruments and adopts quantitative methods, which allow it to consider more complex and realistic economies. Capital taxes are optimal when age-dependent labor income taxes are not possible. The newer and tractable sufficient statistics approach derives robust tax formulas that depend on estimable elasticities and features of the income distributions. It simplifies the transitional dynamics thanks to a newly defined criterion, the utility-based steady-state approach, which prevents the government from exploiting sluggish responses in the short run. Capital taxes are here based on the standard equity-efficiency trade-off.