This literature review assesses the neglected role of invariant representations in grounded cognition approaches. Invariant representations consist of physical invariants (e.g., momentum, gravity, friction) which are internalized and form part of the mental representations of objects. Other features of objects, such as their appearance, tactile feel, or taste are represented in the form of sensorimotor states. In grounded cognition approaches, abstract concepts, which by definition cannot be perceived using the sensorimotor system, nonetheless consist of sensorimotor representations. Following this, invariant representations should also be material in which to ground abstract concepts. The warmth felt when touching a hot cup of coffee is part of the object representation just like the gravity acting upon it when it falls off the table. With grounded cognition becoming a staple of cognitive research, and recent advances in research on invariant representations, this review addresses an overdue question: What is the role of invariant representations in grounding cognition? Most grounded cognition theories include only body-related, sensorimotor experiences. Others (e.g., conceptual metaphor theory) implicitly include invariant representations. Some do not deny, but also do not explicitly mention them (e.g., perceptual symbol systems). Only very few theories mention invariant representations, then as shaping cognition (e.g., the TEST taxonomy), or as an organizing principle of cognition (e.g., Shepard’s ecological constraints). We present a theoretically-unbound summary of literature, describing that the neglect of invariant representations may be unjustified, and we delineate hypotheses addressing critical questions for future progress in this domain.