This paper presents the case for tax progressivity based on recent results in optimal tax theory. We consider the optimal progressivity of earnings taxation and whether capital income should be taxed. We critically discuss the academic research on these topics and when and how the results can be used for policy recommendations. We argue that a result from basic research is relevant for policy only if (a) it is based on economic mechanisms that are empirically relevant and first order to the problem, (b) it is reasonably robust to changes in the modeling assumptions, (c) the policy prescription is implementable (i.e., is socially acceptable and is not too complex). We obtain three policy recommendations from basic research that satisfy these criteria reasonably well. First, very high earners should be subject to high and rising marginal tax rates on earnings. Second, low income families should be encouraged to work with earnings subsidies, which should then be phased-out with high implicit marginal tax rates. Third, capital income should be taxed. We explain why the famous zero marginal tax rate result for the top earner in the Mirrlees model and the zero capital income tax rate results of Chamley-Judd and Atkinson-Stiglitz are not policy relevant in our view.