Eye movements were recorded as 12‐month‐olds (n = 15), 4‐year‐olds (n = 17), and adults (n = 19) watched a 15‐min video with sequences of shots conveying continuous motion. The central question was whether, and at what age, viewers anticipate the reappearance of objects following cuts to new shots. Adults were more likely than younger viewers to make anticipatory eye movements. Four‐year‐olds responded to transitions more slowly and tended to fixate the center of the screen. Infants’ eye movement patterns reflected a tendency to react rather than anticipate. Findings are consistent with the hypothesis that adults integrate content across shots and understand how space is represented in edited video. Results are interpreted with respect to a developing understanding of film editing due to experience and cognitive maturation.