Traditionally, cognition has been considered a uniquely human capability involving perception, memory, learning, reasoning, and problem-solving. However, recent research shows that cognition is a fundamental ability shared by all living beings, from single cells to complex organisms. This chapter takes an info-computational approach (ICON), viewing natural structures as information and the processes of change in these structures as computations. It is a relational framework dependent on the perspective of a cognizing observer/cognizer. Informational structures are properties of the material substrate, and when focusing on the behavior of the substrate, we discuss morphological computing (MC). ICON and MC are complementary perspectives for a cognizer. Information and computation are inseparably connected with cognition. This chapter explores research connecting nature as a computational structure for a cognizer, with morphological computation, morphogenesis, agency, extended cognition, and extended evolutionary synthesis, using examples of the free energy principle and active inference. It introduces theoretical and practical approaches challenging traditional computational models of cognition limited to abstract symbol processing, highlighting the computational capacities inherent in the material substrate (embodiment). Understanding the embodiment of cognition through its morphological computational basis is crucial for biology, evolution, intelligence theory, AI, robotics, and other fields.