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In this paper, we review adversarial pretraining of self-supervised deep networks including both convolutional neural networks and vision transformers. Unlike the adversarial training with access to labeled examples, adversarial pretraining is complicated as it only has access to unlabeled examples. To incorporate adversaries into pretraining models on either input or feature level, we find that existing approaches are largely categorized into two groups: memory-free instance-wise attacks imposing worst-case perturbations on individual examples, and memory-based adversaries shared across examples over iterations. In particular, we review several representative adversarial pretraining models based on Contrastive Learning (CL) and Masked Image Modeling (MIM), respectively, two popular self-supervised pretraining methods in literature. We also review miscellaneous issues about computing overheads, input-/feature-level adversaries, as well as other adversarial pretraining approaches beyond the above two groups. Finally, we discuss emerging trends and future directions about the relations between adversarial and cooperative pretraining, unifying adversarial CL and MIM pretraining, and the trade-off between accuracy and robustness in adversarial pretraining.