Embodied theories of cognition consider many aspects of language and other cognitive domains as the result of sensory and motor processes. In this view, the appraisal and the use of concepts are based on mechanisms of simulation grounded on prior sensorimotor experiences. Even though these theories continue receiving attention and support, increasing evidence indicates the need to consider the flexible nature of the simulation process, and to accordingly refine embodied accounts. In this consensus paper, we discuss two potential sources of variability in experimental studies on embodiment of language: individual differences and context. Specifically, we show how factors contributing to individual differences may explain inconsistent findings in embodied language phenomena. These factors include sensorimotor or cultural experiences, imagery, context-related factors, and cognitive strategies. We also analyze the different contextual modulations, from single words to sentences and narratives, as well as the top-down and bottom-up influences. Similarly, we review recent efforts to include cultural and language diversity, aging, neurodegenerative diseases, and brain disorders, as well as bilingual evidence into the embodiment framework. We address the importance of considering individual differences and context in clinical studies to drive translational research more efficiently, and we indicate recommendations on how to correctly address these issues in future research. Systematically investigating individual differences and context may contribute to understanding the dynamic nature of simulation in language processes, refining embodied theories of cognition, and ultimately filling the gap between cognition in artificial experimental settings and cognition in the wild (i.e., in everyday life).