For describing continuum of natural cognition, from basal cellular to human level, we use evolutionary info-computational framework, where natural/physical/morphological computation drives generation of increasingly adept cognitive systems. We build on novel developments in information physics, bioinformatics, information chemistry, computational neuroscience, complexity theory, self-organization, theory of evolution (new synthesis), information, and computation, a constructive interdisciplinary framework for understanding of cognition in the context of computing nature. Interactions between constituents at different levels of organization lead to complexification of agency and increased cognitive capacities of organisms. Recently, possibility of controlling basal cell cognition attracted a lot of interest for its possible applications in medicine, new computing technologies, as well as micro- and nano-robotics. Bio-cognition of cells connected into tissues/organs and organisms with the group (social) levels of distributed information processing provides insights into cognition mechanisms that can help us to better conceptualize human cognition with its evolution and support the development of new AI models and cognitive robots. It will also give us better understanding of the human as a natural being and our connectedness with the rest of nature.