When people interact, they convey their intentions not only to talk to one another, but to start, maintain and end their interactions. In face-to-face interaction, this process of "engagement" takes place via non-verbal gestures as well as verbal communication. This talk will discuss the engagement process, how people perform part of it through their mutual looking at each other and other objects. The talk will turn to building a robot that can engage in conversation in a similar way to people. I will discuss the architecture for the robot and demonstrate via video clips the interactions of a person with the robot. Finally, I will discuss two studies of users interacting with the robot in a collaborative task, one concerning engagement through mutual looking and the other, the effects of nodding in conversation with the robot.