Concerns about the potential negative effects on domestic firms’ international competitiveness and ensuing carbon leakage are the main obstacle to the unilateral use of carbon pricing for reducing greenhouse gas emissions. Since 2005, the EU Emissions Trading System (EU ETS) has put a price on about half of the EU’s overall emissions and presently remains the largest cap-and-trade scheme in the world. Monitoring the competitiveness effects of the EU ETS is vital for evaluating the cost effectiveness of the policy instrument and for amending it if needed. This paper surveys the econometric literature that tests for the occurrence of competitiveness effects and carbon leakage under the EU ETS. Emphasised is the specific or more general relevance of estimation results for sectors, countries and years. Organised in this way, the empirical evidence may better inform policy. The review also covers several studies analysing the competitiveness effects of the EU ETS through the lens of stock markets. By far, the most frequently encountered conclusion is that no evidence was found of negative statistically significant effects on firms’ competitiveness (nor, therefore, of carbon leakage). Among the few adverse effects, those concerning increased FDI activity in certain regulated sectors deserve special consideration.