Work in Human–Robot Interaction (HRI) has investigated interactions between one human and one robot as well as human–robot group interactions. Yet the field lacks a clear definition and understanding of the influence a robot can exert on interactions between other group members (e.g., human-to-human). In this article, we define Interaction-Shaping Robotics (ISR), a subfield of HRI that investigates robots that influence the behaviors and attitudes exchanged between two (or more) other agents. We highlight key factors of interaction-shaping robots that include the role of the robot, the robot-shaping outcome, the form of robot influence, the type of robot communication, and the timeline of the robot’s influence. We also describe three distinct structures of human–robot groups to highlight the potential of ISR in different group compositions and discuss targets for a robot’s interaction-shaping behavior. Finally, we propose areas of opportunity and challenges for future research in ISR.