Sensorimotor representations are essential for building up and maintaining corporeal awareness, i.e. the ability to perceive, know and evaluate one's own body as well as the bodies of others. The notion of embodied cognition implies that abstract forms of conceptual knowledge may be ultimately instantiated in such sensorimotor representations. In this sense, conceptual thinking should evoke, via mental simulation, some underlying sensorimotor events. In this review we discuss studies on the relation between embodiment and corporeal awareness. We approach the question (...) by issuing challenges from both ends. First, we ask whether bodily representations themselves can be disembodied or disconnected from underlying sensorimotor events. Second, we ask whether any concept, no matter how abstract, can actually be embodied in this way. The strong view of embodied cognition requires a negative answer to the first question, and an affirmative answer to the second. We also focus on the surprising range of cognitive processes that can be explained by linking them to corporeal awareness, such as aesthetic appreciation, and object constancy following brain damage. We conclude that (a) somatomotor simulation may help to understand the external world and the society of other individuals, but (b) some non-somatic forms of simulation may be required to explain how abstract knowledge contributes to understanding others' states. In this sense, the classic divide between sensorimotor and conceptual domains must remain in some form. (shrink)