How are abstract concepts such as 'freedom' and 'democracy' represented in the mind? One prominent proposal suggests that abstract concepts are grounded in emotion. Supporting this 'affective embodiment' account, abstract concepts are rated to be more strongly positive or more strongly negative than concrete concepts. This paper demonstrates that this finding generalizes across languages by synthesizing rating data from Cantonese, Mandarin Chinese, Croatian, Dutch, French, German, Indonesian, Italian, Polish and Spanish. However, a deeper look at the same data suggests that the idea of emotional grounding only characterizes a small subset of abstract concepts. Moreover, when the concreteness/abstractness dimension is not operationalized using concreteness ratings, it is actually found that concrete concepts are rated as more emotional than abstract ones. Altogether, these results suggest limitations to the idea that emotion is an important factor in the grounding of abstract concepts. This article is part of the theme issue 'Concepts in interaction: social engagement and inner experiences'.