This thesis presents possible computational mechanisms by which a humanoid robot can develop a coherent representation of the space within its reach (its peripersonal space), and use it to control its movements. Those mechanisms are inspired by current theories of peripersonal space representation and motor control in humans, targeting a cross-fertilization between robotics on one side, and cognitive science on the other side. This research addresses the issue of adaptivity the sensorimotor level, at the control level and at the level of simple task learning. First, this work considers the concept of body schema and suggests a computational translation of this concept, appropriate for controlling a humanoid robot. This model of the body schema is adaptive and evolves as a result of the robot sensory experience. It suggests new avenues for understanding various psychophysical and neuropsychological phenomenons of human peripersonal space representation such as adaptation to distorted vision and tool use, fake limbs experiments, body-part centered receptive fields, and multimodal neurons. Second, it is shown how the motor modality can be added to the body schema. The suggested controller is inspired by the dynamical system theory of motor control and allows the robot to simultaneously and robustly control its limbs in joint angles space and in end-effector location space. This amounts to controlling the robot in both proprioceptive and visual modalities. This multimodal control can benefit from the advantages offered by each modality and is better than traditional robotic controllers in several respects. It offers a simple and elegant solution to the singularity and joint limit avoidance problems and can be seen as a generalization of the Damped Least Square approach to robot control. The controller exhibits several properties of human reaching movements, such as quasi-straight hand paths and bell-shaped velocity profiles and non-equifinality. In a third step, the motor modalities is endowed with a statistical learning mechanism, based on Gaussian Mixture Models, that enables the humanoid to learn motor primitives from demonstrations. The robot is thus able to learn simple manipulation tasks and generalize them to various context, in a way that is robust to perturbations occurring during task execution. In addition to simulation results, the whole model has been implemented and validated on two humanoid robots, the Hoap3 and the iCub, enabling them to learn their arm and head geometries, perform reaching movements, adapt to unknown tools, and visual distortions, and learn simple manipulation tasks in a smooth, robust and adaptive way. Finally, this work hints at possible computational interpretations of the concepts of body schema, motor perception and motor primitives.