We survey the theoretical and empirical literature on local and international tax competition in Economics. Based on this survey, we discuss whether EU countries should harmonize tax policies to prevent a race to the bottom. Much of the evidence suggests that tax competition does not lead to significant reductions in tax revenues. Therefore, we conclude that tax coordination is in all likelihood unnecessary to prevent inefficiently low levels of taxation in the EU. But since the evidence against adverse effects of tax competition is not unambiguous, we also discuss whether intergovernmental transfers might be a less invasive means than outright tax harmonization to prevent a race to the bottom.