The promotion of low carbon energy and associated infrastructures for tackling climate change is a central task for governments worldwide. However, public and, mainly, local, opposition to those infrastructures may slow down or even halt that process. Thus, in the last few years a body of research has developed specifically to understand the social acceptance of technologies such as wind turbines or bioenergy plants. We argue that the use of 'acceptance' in this literature should be further discussed. We contend that using the word 'acceptance' may present some constraints for the theoretical advancement of this area of research and to the implications that may be taken from it to the wider society. This is further highlighted through the presentation of findings from surveys conducted with nationally representative samples from the UK and Norway which examined their acceptance of and support for new high voltage power lines. We conclude by suggesting that the literature on public responses towards low carbon energy and associated infrastructures should be more critical in the conceptualisation of its research agenda, become empirically more consistent and transparent, and examine other types of relations between people and energy infrastructures besides acceptance or opposition.