The concept of green growth rests on the idea of an efficiency revolution: green and climate-friendly innovations, huge investments to restructure the industrial, building and transport sectors, and a boost for using resources and energy more productively and efficiently. This study explores a fatal fallacy of the notion of green growth: while vast productivity increases do indeed incentivise a more efficient use of energy (and resources), they also raise demand. This rebound effect nullifies a considerable proportion of the savings potential of efficiency technologies and measures. Moreover, although the causal link between increased energy productivity and increased demand is well-established, rebound effects are still ignored in the majority of energy and climate studies and policies. This paper explores a range of possible rebound effects, outlines their quantitative extent and describes the difficulties encountered by political efforts to contain them.