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This study aims to place Lorenzo Magnani’s Eco-Cognitive Computationalism within the broader context of current work on information, computation, and cognition. Traditionally, cognition was believed to be exclusive to humans and a result of brain activity. However, recent studies reveal it as a fundamental characteristic of all life forms, ranging from single cells to complex multicellular organisms and their networks. Yet, the literature and general understanding of cognition still largely remain human-brain-focused, leading to conceptual gaps and incoherency. This paper presents a variety of computational (information processing) approaches, including an info-computational approach to cognition, where natural structures represent information and dynamical processes on natural structures are regarded as computation, relative to an observing cognizing agent. We model cognition as a web of concurrent morphological computations, driven by processes of self-assembly, self-organization, and autopoiesis across physical, chemical, and biological domains. We examine recent findings linking morphological computation, morphogenesis, agency, basal cognition, extended evolutionary synthesis, and active inference. We establish a connection to Magnani’s Eco-Cognitive Computationalism and the idea of computational domestication of ignorant entities. Novel theoretical and applied insights question the boundaries of conventional computational models of cognition. The traditional models prioritize symbolic processing and often neglect the inherent constraints and potentialities in the physical embodiment of agents on different levels of organization. Gaining a better info-computational grasp of cognitive embodiment is crucial for the advancement of fields such as biology, evolutionary studies, artificial intelligence, robotics, medicine, and more.