Embodied predictive processing accounts place the visceral milieu, its homeostatic functioning, and our interoceptive awareness thereof on the center stage of self-awareness. Starting from the privileged status that homeostatic priors have within the cortical hierarchy of an organism whose main imperative is to maintain homeostasis, we focus on the mechanisms that underlie interoceptive precision and its impact on embodiment and cognition. Beyond their privileged status for ensuring the stability of organism, this chapter considers the psychological importance that interoceptive priors and interoceptive precision have for self-awareness and the grounding of a coherent self-model. In a manner analogous to the role that interoception plays for homeostasis, interoception at the psychological level seems to contribute to the stability of self-awareness. This psychological role of interoception is illustrated by a growing body of research that considers the antagonism but also the integration between exteroceptive and interoceptive models of the self.