Cognition, historically considered uniquely human capacity, has been recently found to be the ability of all living organisms, from single cells and up. This study approaches cognition from an info-computational stance, in which structures in nature are seen as information, and processes (information dynamics) are seen as computation, from the perspective of a cognizing agent. Cognition is understood as a network of concurrent morphological/morphogenetic computations unfolding as a result of self-assembly, self-organization, and autopoiesis of physical, chemical, and biological agents. The present-day human-centric view of cognition still prevailing in major encyclopedias has a variety of open problems. This article considers recent research about morphological computation, morphogenesis, agency, basal cognition, extended evolutionary synthesis, free energy principle, cognition as Bayesian learning, active inference, and related topics, offering new theoretical and practical perspectives on problems inherent to the old computationalist cognitive models which were based on abstract symbol processing, and unaware of actual physical constraints and affordances of the embodiment of cognizing agents. A better understanding of cognition is centrally important for future artificial intelligence, robotics, medicine, and related fields.