Searching for an understanding of how the brain supports conscious processes, cognitive scientists have proposed two main classes of theory: Global Workspace and Information Integration theories. These theories seem to be complementary, but both still lack grounding in terms of brain mechanisms responsible for the production of coherent and unitary conscious states. Here we propose - following James Robertson's "Astrocentric Hypothesis' - that conscious processing is based on analog computing in astrocytes. The "hardware" for these computations is calcium waves mediated by adenosine triphosphate signaling. Besides presenting our version of this hypothesis, we also review recent findings on astrocyte morphology that lend support to their functioning as Local Hubs (composed of protoplasmic astrocytes) that integrate synaptic activity, and as a Master Hub (composed, in the human brain, by a combination of interlaminar, fibrous, polarized and varicose projection astrocytes) that integrates whole-brain activity.