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We show that there may exist an inherent tension between the goal of adversarial robustness and that of standard generalization. Specifically, training robust models may not only be more resource-consuming, but also lead to a reduction of standard accuracy. We demonstrate that this trade-off between the standard accuracy of a model and its robustness to adversarial perturbations provably exists in a fairly simple and natural setting. These findings also corroborate a similar phenomenon observed empirically in more complex settings. Further, we argue that this phenomenon is a consequence of robust classifiers learning fundamentally different feature representations than standard classifiers. These differences, in particular, seem to result in unexpected benefits: the representations learned by robust models tend to align better with salient data characteristics and human perception.