Successful linguistic communication relies on a shared experience of the world, and it is this shared experience that makes utterances meaningful. Despite the incredible effectiveness of language processing models trained on text alone, today's best systems still make mistakes that arise from a failure to relate language to the physical world it describes and to the social interactions it facilitates. Natural Language Processing is a diverse field, and progress throughout its development has come from new representational theories, modeling techniques, data collection paradigms, and tasks. We posit that the present success of representation learning approaches trained on large text corpora can be deeply enriched from the parallel tradition of research on the contextual and social nature of language. In this article, we consider work on the contextual foundations of language: grounding, embodiment, and social interaction. We describe a brief history and possible progression of how contextual information can factor into our representations, with an eye towards how this integration can move the field forward and where it is currently being pioneered. We believe this framing will serve as a roadmap for truly contextual language understanding.