Bodily self-attribution, the feeling that a body (or parts of it) is owned by me, is a fundamental component of one's self. Previous studies have suggested that, in addition to a necessary multi-sensory stimulation, the sense of body ownership is determined by the body model, a representation of our body in the brain. It is however unclear what features constitute the body representation. To examine this issue, we first briefly review results on embodiment of artificial limbs, whole bodies and virtual avatars to understand the apparent anatomical, volumetric and spatial constraints associated with the sense of ownership toward external entities. We then discuss how considering limb functionality in the body model can provide an integrated explanation for most of the varied embodiment results in literature. We propose that the self-attribution of an entity may be determined, not just by its physical features, but by whether the entity can afford actions that the brain has associated with the limb which it replaces.