Significant efforts have been made in the past decades to understand how mental and cognitive processes are underpinned by neural mechanisms in the brain. This paper argues that a promising way forward in understanding the nature of human cognition is to zoom out from the prevailing picture focusing on its neural basis. It considers instead how neurons work in tandem with other type of cells (e.g., immune) to subserve biological self-organization and adaptive behavior of the human organism as a whole. We focus specifically on the immune cellular processing as key actor in complementing neuronal processing in achieving successful self-organization and adaptation of the human body in an ever-changing environment. We overview theoretical work and empirical evidence on “basal cognition” challenging the idea that only the neuronal cells in the brain have the exclusive ability to “learn” or “cognize.” The focus on cellular rather than neural, brain processing underscores the idea that flexible responses to fluctuations in the environment require a carefully crafted orchestration of multiple cellular and bodily systems at multiple organizational levels of the biological organism. Hence cognition can be seen as a multiscale web of dynamic information processing distributed across a vast array of complex cellular (e.g., neuronal, immune, and others) and network systems, operating across the entire body, and not just in the brain. Ultimately, this paper builds up toward the radical claim that cognition should not be confined to one system alone, namely, the neural system in the brain, no matter how sophisticated the latter notoriously is.