concepts, like justice and friendship, are central features of our daily lives. Traditionally, abstract concepts are distinguished from other concepts in that they cannot be directly experienced through the senses. As such, they pose a challenge for strongly embodied models of semantic representation that assume a central role for sensorimotor information. There is growing recognition, however, that it is possible for meaning to be 'grounded' via cognitive systems, including those involved in processing language and emotion. In this article, we focus on the specific proposal that social significance is a key feature in the representation of some concepts. We begin by reviewing recent evidence in favour of this proposal from the fields of psycholinguistics and neuroimaging. We then discuss the limited extent to which there is consensus about the definition of 'socialness' and propose essential next steps for research in this domain. Taking one such step, we describe preliminary data from an unprecedented large-scale rating study that can help determine how socialness is distinct from other facets of word meaning. We provide a backdrop of contemporary theories regarding semantic representation and social cognition and highlight important predictions for both brain and behaviour. This article is part of the theme issue 'Concepts in interaction: social engagement and inner experiences'.