This paper carefully surveys the econometric literature that tests for competitiveness effects and related carbon leakage caused by the EU Emissions Trading System (EU ETS). The results of this literature tell us that to date there is no evidence of the EU ETS having had widespread negative or positive effects on the competitiveness of regulated firms, nor is there evidence of significant carbon leakage. However, the paper also identifies three important caveats to this general conclusion. Firstly, the evidence we have still largely refers to the first two trading periods, namely Phases I (2005–2007) and II (2008–2012). Secondly, some heterogeneity of estimated effects is observed, but patterns, notably sectoral patterns, hardly emerge. Thirdly, very little explored is whether the EU ETS has had long‐term effects on the economy via investment leakage or firm dynamics. Further empirical studies investigating these long‐term effects are particularly desirable.