The increasing sophistication of NLP models has renewed optimism regarding machines achieving a full human-like command of natural language. Whilst work in NLP/NLU may have made great strides in that direction, the lack of conceptual clarity in how 'understanding' is used in this and other disciplines have made it difficult to discern how close we actually are. A critical, interdisciplinary review of current approaches and remaining challenges is yet to be carried out. Beyond linguistic knowledge, this requires considering our species-specific capabilities to categorize, memorize, label and communicate our (sufficiently similar) embodied and situated experiences. Moreover, gauging the practical constraints requires critically analyzing the technical capabilities of current models, as well as deeper philosophical reflection on theoretical possibilities and limitations. In this paper, I unite all of these perspectives -- the philosophical, cognitive-linguistic, and technical -- to unpack the challenges involved in approaching true (human-like) language understanding. By unpacking the theoretical assumptions inherent in current approaches, I hope to illustrate how far we actually are from achieving this goal, if indeed it is the goal.