Deep neural networks have revolutionized computer vision, and their object representations across layers match coarsely with visual cortical areas in the brain. However, whether these representations exhibit qualitative patterns seen in human perception or brain representations remains unresolved. Here, we recast well-known perceptual and neural phenomena in terms of distance comparisons, and ask whether they are present in feedforward deep neural networks trained for object recognition. Some phenomena were present in randomly initialized networks, such as the global advantage effect, sparseness, and relative size. Many others were present after object recognition training, such as the Thatcher effect, mirror confusion, Weber’s law, relative size, multiple object normalization and correlated sparseness. Yet other phenomena were absent in trained networks, such as 3D shape processing, surface invariance, occlusion, natural parts and the global advantage. These findings indicate sufficient conditions for the emergence of these phenomena in brains and deep networks, and offer clues to the properties that could be incorporated to improve deep networks.