Endogenous demand responses for energy services, resulting from changing prices, have long been characterised in energy systems models. However, the uncertainty associated with such demand responses, modelled through the use of price elasticities, has often been ignored. This is problematic for two key reasons - elasticity factors used in models are highly uncertain due to the limited evidence base, while at the same time, demand response has been observed as a critical mechanism for meeting long term climate mitigation targets. This paper makes two important contributions for improving the understanding of the role of price-induced demand response. Firstly, it attempts to address the problem of unsatisfactory elasticity input assumptions by undertaking an up-to-date review of the literature. Secondly, the role of demand response under uncertainty is assessed using a probabilistic approach, focusing on its contribution to mitigation. The paper highlights that demand response does play a critical role in mitigation, ensuring a more cost-effective transition to a low carbon energy system. Crucially, the uncertainties associated with price elasticities do not weaken this finding. The transport sector is the driver of this demand response leading to important implications for policy and the focus of demand side interventions. (C) 2014 Elsevier Ltd. All rights reserved.