This paper investigates the relationships between energy efficiency improvements by producers, the ease of substitution between energy and other inputs and the size of the resulting “rebound effects”. Fundamentally, easier substitution leads to larger rebounds. Focusing upon conceptual and methodological issues, the paper highlights the challenges of estimating and modeling rebound effects with the help of production and cost functions and questions the robustness of the evidence base in this area. It argues that the multiple definitions of “elasticities of substitution” are a source of confusion, the most commonly estimated elasticity is of little practical value, the empirical literature is contradictory, prone to bias and difficult to use and there are only tenuous links between this literature and the assumptions used within energy-economic models. While “energy-augmenting technical change” provides the natural choice of independent variable for an estimate of rebound effects, most empirical studies do not estimate this form of technical change, many modeling studies do not simulate it and others simulate it in such a way as to underestimate rebound effects. As a result, the paper argues that current econometric and modeling studies do not provide reliable guidance on the magnitude of rebound effects in different industrial sectors.