I introduce arguments toward a non-representational reflexivity theory of consciousness-as-such to address one of the key issues in the science of consciousness today: lack of understanding of the nature of consciousness itself. An expanded map of consciousness is outlined, which includes, in addition to the well-known contents of awareness and levels of arousal, the indeterminate substrate and consciousness-as-such or nondual awareness. The central idea presented is that consciousness-as-such is a non-conceptual nondual awareness, whose essential property is non-representational reflexivity. This property makes consciousness-as-such phenomenologically, cognitively and neurobiologically a unique kind, different from and irreducible to any contents, functions and states, including the indeterminate substrate. Our previous hypothesis on the precuneus network for nondual awareness is further discussed in relation to non-representational reflexivity, and in the light of other hypotheses on the neural correlates of consciousness-as-such.