Resonance, a powerful and pervasive phenomenon, appears to play a major role in human interactions. This article investigates the relationship between the physical mechanism of resonance and the human experience of resonance, and considers possibilities for enhancing the experience of resonance within human–robot interactions. We first introduce resonance as a widespread cultural and scientific metaphor. Then, we review the nature of “sympathetic resonance” as a physical mechanism. Following this introduction, the remainder of the article is organized in two parts. In part one, we review the role of resonance (including synchronization and rhythmic entrainment) in human cognition and social interactions. Then, in part two, we review resonance-related phenomena in robotics and artificial intelligence (AI). These two reviews serve as ground for the introduction of a design strategy and combinatorial design space for shaping resonant interactions with robots and AI. We conclude by posing hypotheses and research questions for future empirical studies and discuss a range of ethical and aesthetic issues associated with resonance in human–robot interactions.