Residential demand response (meaning changes to electricity use at specific times) has been proposed as an important part of the low carbon energy system transition. Modelling studies suggest benefits may include deferral of distribution network reinforcement, reduced curtailment of wind generation, and avoided investment in reserve generation. To accurately assess the contribution of demand response such studies must be supported by realistic assumptions on consumer participation. A systematic review of international evidence on trials, surveys and programmes of residential demand response suggests that it is important that these assumptions about demand response are not overly optimistic. Customer participation in trials and existing programmes is often 10% or less of the target population, while responses of consumers in existing schemes have varied considerably for a complex set of reasons. Relatively little evidence was identified for engagement with more dynamic forms of demand response, making its wider applicability uncertain. The evidence suggests that the high levels of demand response modelled in some future energy system scenarios may be more than a little optimistic. There is good evidence on the potential of some of the least ‘smart’ options, such as static peak pricing and load control, which are well established and proven. More research and greater empirical evidence is needed to establish the potential role of more innovative and dynamic forms of demand response.