Convolutional neural networks (CNNs) are increasingly used to model human vision due to their high object categorization capabilities and general correspondence with human brain responses. Here we evaluate the performance of 14 different CNNs compared with human fMRI responses to natural and artificial images using representational similarity analysis. Despite the presence of some CNN-brain correspondence and CNNs’ impressive ability to fully capture lower level visual representation of real-world objects, we show that CNNs do not fully capture higher level visual representations of real-world objects, nor those of artificial objects, either at lower or higher levels of visual representations. The latter is particularly critical, as the processing of both real-world and artificial visual stimuli engages the same neural circuits. We report similar results regardless of differences in CNN architecture, training, or the presence of recurrent processing. This indicates some fundamental differences exist in how the brain and CNNs represent visual information.