According to embodied theories (including embodied, embedded, extended, enacted, situated, and grounded approaches to cognition), language representation is intrinsically linked to our interactions with the world around us, which is reflected in specific brain signatures during language processing and learning. Moving on from the original rivalry of embodied vs. amodal theories, this consensus paper addresses a series of carefully selected questions that aim at determining when and how rather than whether motor and perceptual processes are involved in language processes. We cover a wide range of research areas, from the neurophysiological signatures of embodied semantics, e.g., event-related potentials and fields as well as neural oscillations, to semantic processing and semantic priming effects on concrete and abstract words, to first and second language learning and, finally, the use of virtual reality for examining embodied semantics. Our common aim is to better understand the role of motor and perceptual processes in language representation as indexed by language comprehension and learning. We come to the consensus that, based on seminal research conducted in the field, future directions now call for enhancing the external validity of findings by acknowledging the multimodality, multidimensionality, flexibility and idiosyncrasy of embodied and situated language and semantic processes.