As part of the technological transformation of societies, embodied digital technologies (EDTs) such as autonomous service and delivery robots, socially interactive robots, self-driving cars, virtual (service) agents, “intelligent” wearables, and protheses (to name only a few) have become a part of our daily lives and will further proliferate in the future, with wide-ranging implications for human-technology interaction. EDTs are artificial agents that are physically represented in areas previously only occupied by humans. We use the term hybrid societies for future societies in which humans, human-technological hybrids, and EDTs interact and share public spaces (e.g., roads, sidewalks, malls, and public buildings). Specifically, we define a hybrid society as a collective of embodied agents (including humans, partly human actors such as cyborgs, and non-human EDTs such as robots) with the capability to engage in intelligible encounters, who interact and communicate, who can meaningfully reference each other as members of society, and who vary in terms of autonomy, agency, and responsibility. We propose that psychological and technological factors governing effective interactions among humans and EDTs in hybrid societies can be subsumed under two research questions: (1) How do humans perceive and interact with embodied technologies? (2) What are design principles and strategies for designing accountable embodied technology, i.e., embodied technologies that effectively signal to others who encounter them what they can do, want, and how one is supposed to interact with them? We lay out a research agenda for addressing these questions and discuss potential implications.