Deep artificial neural networks are promising computational models of the human ventral visual system. Neural networks show impressive performance on image recognition tasks. Furthermore, they account for significant proportions of variance in human brain responses and behavior measured during image recognition tasks. However, neural networks also fail to account for significant proportions of variance in human responses to images, especially during more naturalistic visual tasks such as recognizing objects under occlusion. I will show work from my lab that highlights both the potential and the shortcomings of contemporary neural networks as models of human vision. I will argue for the need for a more human-like learning experience, including a more naturalistic visual diet and learning goals, to transform neural networks from powerful image recognizers to human-like object perceivers.