Little is known about the development of higher-level areas of visual cortex during infancy, and even less is known about how the development of visually guided behavior is related to the different levels of the cortical processing hierarchy. As a first step toward filling these gaps, we used representational similarity analysis (RSA) to assess links between gaze patterns and a neural network model that captures key properties of the ventral visual processing stream. We recorded the eye movements of 4- to 12-month-old infants (N = 54) as they viewed photographs of scenes. For each infant, we calculated the similarity of the gaze patterns for each pair of photographs. We also analyzed the images using a convolutional neural network model in which the successive layers correspond approximately to the sequence of areas along the ventral stream. For each layer of the network, we calculated the similarity of the activation patterns for each pair of photographs, which was then compared with the infant gaze data. We found that the network layers corresponding to lower-level areas of visual cortex accounted for gaze patterns better in younger infants than in older infants, whereas the network layers corresponding to higher-level areas of visual cortex accounted for gaze patterns better in older infants than in younger infants. Thus, between 4 and 12 months, gaze becomes increasingly controlled by more abstract, higher-level representations. These results also demonstrate the feasibility of using RSA to link infant gaze behavior to neural network models. A video abstract of this article can be viewed at https://youtu.be/K5mF2Rw98Is