Three studies investigated infants’ understanding that gaze involves a relation between a person and the object of his or her gaze. Infants were habituated to an event in which an actor turned and looked at one of two toys. Then, infants saw test events in which (1) the actor turned to the same side as during habituation to look at a different toy, or (2) the actor turned to the other side to look at the same toy as during habituation. The first of these involved a change in the relation between actor and object. The second involved a new physical motion on the part of the actor but no change in the relation between actor and object. Seven- and 9-month-old infants did not respond to the change in relation between actor and object, although infants at both ages followed the actor's gaze to the toys. In contrast, 12-month-old infants responded to the change in the actor–object relation. Control conditions verified that the paradigm was a sensitive index of the younger infants’ representations of action: 7- and 9-month-olds responded to a change in the actor–object relation when the actor's gaze was accompanied by a grasp. Taken together, these findings indicate that gaze-following does not initially go hand in hand with understanding the relation between a person who looks and the object of his or her gaze, and that infants begin to understand this relation between 9 and 12 months.