This theme issue aims to view the literature on concepts through a novel lens, that of social interaction and its influence on inner experiences. It discusses unsolved problems in literature on concepts, emphasizing the distinction between concrete versus abstract concepts and external versus internal grounding. This introductory article reflects the two research streams that the theme aims to bridge - in this area, the dimension of embodied interaction with others and how this influences the interaction with ourselves is still underexplored. In the first part, we discuss recent trends in social cognition, showing how interacting with others influences our concepts. In the second part, we address how social interactions become part of our inner world in a Vygotskian fashion. First, we illustrate how interoception, emotion and metacognition are connected with concepts and knowledge. Second, we deal with how language, in both its outer and inner form, can empower cognition and concepts. We also briefly describe how novel experimental and computational methods contribute to investigating the online use of concepts. Overall, this introductory article outlines the potentialities of an integrated and interactive approach that can give new, fresh life to a topic, that of concepts, which lies at the root of human cognition. This article is part of the theme issue 'Concepts in interaction: social engagement and inner experiences'.