The fields of artificial intelligence and bio-inspired robotics have proven to cross several other fields of expertise including Cognitive Neuroscience. Here, we review principles of interaction between a natural (or artificial) organism and the environment where it lives. Then we ask whether such structural coupling shapes the way it behaves. For instance, how the sensory processing of the external world controls actions, and finally, behavior? We remind the main sources of inspiration for bio-inspired robotics and relate them to currently active fields of research like Embodiment and Enaction. These latter concepts are illustrated by examples of recent researches on two main aspects: (i) bio-inspired algorithms processing sensory signals coming from the outer world and (ii) bio-inspired controllers based on human behavior and physiology. Finally, we include an example of a bio-inspired robot controller design based on the concepts here exposed.