Fueled by innovation in the computer vision and artificial intelligence communities, recent developments in computational neuroscience have used goal-driven hierarchical convolutional neural networks (HCNNs) to make strides in modeling neural single-unit and population responses in higher visual cortical areas. In this Perspective, we review the recent progress in a broader modeling context and describe some of the key technical innovations that have supported it. We then outline how the goal-driven HCNN approach can be used to delve even more deeply into understanding the development and organization of sensory cortical processing.