This paper reviews the empirical literature analysing the effects of the EU Emissions Trading System (EU ETS) on low-carbon technological change. The emerging evidence is assessed, with references to both relevant economic concepts and the evolving regulation of the EU ETS through time. The two most robust indications of the literature are: a) the EU ETS appears to have been more effective in stimulating innovation of low-carbon technologies rather than their adoption; and b) free allocation (grandfathering) tended to hamper low-carbon investments in Phases I (2005-2007) and II (2008-2012). However, a complete general picture of the impact of the EU ETS on low-carbon technological change is missing. The main gap regards the lack of empirical evidence for Phase III (2013-2020). Especially econometric studies are few, due to the lack of suitable databases accessible to researchers - a problem that the relevant public authorities are urged to address. Thanks to the recent reforms of the EU ETS, the incentives for innovation and adoption of low-carbon technologies are probably stronger today than ever before.