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Humans have the fascinating capacity of processing nonverbal visual cues to understand and anticipate the actions of other humans. This 'intention reading' ability is underpinned by shared motor repertoires and action models, which we use to interpret the intentions of others as if they were our own. We investigate how different cues contribute to the legibility of human actions during interpersonal interactions. Our first contribution is a publicly available dataset with recordings of human body motion and eye gaze, acquired in an experimental scenario with an actor interacting with three subjects. From these data, we conducted a human study to analyze the importance of different nonverbal cues for action perception. As our second contribution, we used motion/gaze recordings to build a computational model describing the interaction between two persons. As a third contribution, we embedded this model in the controller of an iCub humanoid robot and conducted a second human study, in the same scenario with the robot as an actor, to validate the model's 'intention reading' capability. Our results show that it is possible to model (nonverbal) signals exchanged by humans during interaction, and how to incorporate such a mechanism in robotic systems with the twin goal of being able to 'read' human action intentionsand acting in a way that is legible by humans. © 2016 IEEE.