This paper summarizes findings on the growing field of role assignment policies for human–robot motor interaction. This topic has been investigated by researchers in the psychological theory of joint action, in human intention detection, force control, human–human physical interaction, as well as roboticists interested in developing robots with capabilities for efficient motor interaction with humans. Our goal is to promote fruitful interaction between these distinct communities by: ( i) examining the role assignment policies for human–robot joint motor action in experimental psychology and robotics studies; and ( ii) informing researchers in human–human interaction on existing work in the robotic field. After an overview of roles assignment in current robotic assistants, this paper examines key results about shared control between a robot and a human performing interactive motor tasks. Research on motor interaction between two humans has inspired recent developments that may extend the use of robots to applications requiring continuous mechanical interaction with humans.