According to grounded cognition, words whose semantics contain sensory-motor features activate sensory-motor simulations, which, in turn, interact with spatial responses to produce grounded congruency effects (e.g., processing the spatial feature of "up" for sky should be faster for up vs. down responses). Growing evidence shows these congruency effects do not always occur, suggesting instead that the grounded features in a word's meaning do not become active automatically across contexts. Researchers sometimes use this as evidence that concepts are not grounded, further concluding that grounded information is peripheral to the amodal cores of concepts. We first review broad evidence that words do not have conceptual cores, and that even the most salient features in a word's meaning are not activated automatically. Then, in three experiments, we provide further evidence that grounded congruency effects rely dynamically on context, with the central grounded features in a concept becoming active only when the current context makes them salient. Even when grounded features are central to a word's meaning, their activation depends on task conditions.