Tax rates on capital income, corporate income tax rates in particular, have been declining in most industrialized countries since the mid 1980ies. Among the explanations for this development tax competition between countries for mobile capital has been mentioned frequently. A vast empirical literature dealing with tax competition for mobile capital has emerged. This paper gives a comprehensive overview of these empirical studies. A particular focus is put on studies modelling strategic interaction in tax policies of competing jurisdictions - which is at the heart of the competition concept. The paper also addresses the issue whether existing studies convincingly isolate tax competition as a driver of falling capital / corporate income tax rates. Given the empirical evidence surveyed it appears that tax rates indeed fall due to tax competition, in particular due to competition for new firms and for paper profits. However, closer look at the empirical approaches applied in the papers surveyed suggests that fully convincing evidence establishing tax competition as driver of falling tax rates is still lacking. / Series: Discussion Papers SFB International Tax Coordination