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This paper explores the concept of engagement, the process by which individuals in an interaction start, maintain and end their perceived connection to one another. The paper reports on one aspect of engagement among human interactors—the effect of tracking faces during an interaction. It also describes the architecture of a robot that can participate in conversational, collaborative interactions with engagement gestures. Finally, the paper reports on findings of experiments with human participants who interacted with a robot when it either performed or did not perform engagement gestures. Results of the human–robot studies indicate that people become engaged with robots: they direct their attention to the robot more often in interactions where engagement gestures are present, and they find interactions more appropriate when engagement gestures are present than when they are not.