This review is the result of a joint reflection carried out by researchers in the fields of robotics and automatic control on the one hand and neuroscience on the other, both trying to answer the same question: what are the functional bases of bipedal locomotion and how can they be controlled? The originality of this work is to synthesize the two approaches in order to take advantage of the knowledge concerning the adaptability and reactivity performances of humans and of the rich tools and formal concepts available in biped robotics. Indeed, we claim that the theoretical framework of robotics can enhance our understanding of human postural control by formally expressing the experimental concepts used in neuroscience. Conversely, biological knowledge of human posture and gait can inspire biped robot design and control. Therefore, both neuroscientists and roboticists should find useful information in this paper.