The design of robots that interact autonomously with the environment and exhibit complex behaviours is an open challenge that can benefit from understanding what makes living beings fit to act in the world. Neuromorphic engineering studies neural computational principles to develop technologies that can provide a computing substrate for building compact and low-power processing systems. We discuss why endowing robots with neuromorphic technologies - from perception to motor control - represents a promising approach for the creation of robots which can seamlessly integrate in society. We present initial attempts in this direction, highlight open challenges, and propose actions required to overcome current limitations.