The thesis presents an approach to social interaction and communication that tries to straddle the divide between Radical Embodied Cognition (REC) and Traditional Cognitive Science (TCS). The former typically holds that cognition is a matter of brain-body-environment systems engaged in adaptive behavior, while for the latter adaptive behavior is an outcome of processing mental representations (of the world and other people). The difference in fundamental views on cognition leads to an adoption of different target explananda and methodologies. This, in turn, results in two distinct bodies of research that cannot be easily compared and evaluated side by side thereby preventing a wider uptake of REC ideas. This thesis attempts to remedy this situation by tackling three issues: (1) the model of explanation adopted by REC and the phenomena it is allegedly unfit to explain, i.e. (2) joint action and (3) language. First, it is argued that a REC approach can be fruitfully combined with one of the dominant TCS explanatory frameworks that of mechanistic explanation. Second, REC is extended to a type of social interaction typically seen by TCS-ers as lying beyond REC’s reach — that of joint action, an activity of several individuals of accomplishing a shared goal in a coordinated manner. Subsequently, two case studies are examined by applying REC principles to two TCS experimental paradigms on joint action. In a reported behavioral study it is found that an experimental effect that is taken to be evidence for representation of the other’s part in the common task (co-representation) does not arise when the paradigm is rendered more embodied. In a simulation study it is found that artificial agents without a built-in co-representation ability accomplish the task that is said to require it. Finally, a proposal is presented as to how REC could be scaled up to language.