Title: Test-Time Adaptation and Adversarial Robustness. Abstract: This paper studies test-time adaptation in the context of adversarial robustness. We formulate an adversarial threat model for test-time adaptation, where the defender may have a unique advantage as the adversarial game becomes a maximin game, instead of a minimax game as in the classic adversarial robustness threat model. We then study whether the maximin threat model admits more ``good solutions'' than the minimax threat model, and is thus \emph{strictly weaker}. For this purpose, we first present a provable separation between the two threat models in a natural Gaussian data model. For deep learning, while we do not have a proof, we propose a candidate, Domain Adversarial Neural Networks (${\sf DANN}$), an algorithm designed for unsupervised domain adaptation, by showing that it provides nontrivial robustness in the test-time maximin threat model against strong transfer attacks and adaptive attacks. This is somewhat surprising since ${\sf DANN}$ is not designed specifically for adversarial robustness (e.g., against norm-based attacks), and provides no robustness in the minimax model. Complementing these results, we show that recent data-oblivious test-time adaptations can be easily attacked even with simple transfer attacks. We conclude the paper with various future directions of studying adversarially robust test-time adaptation.