Title: Online Continual Learning  Under  Domain Shift. Abstract: Existing continual learning benchmarks often assume each task's training and test data are from the same distribution, which may not hold in practice. Towards making continual learning practical, in this paper, we introduce a novel setting of online continual learning under conditional domain shift, in which domain shift exists between training and test data of all tasks: $P^{tr}(X, Y) \neq P^{te}(X,Y)$, and the model is required to generalize to unseen domains at test time. To address this problem, we propose \emph{Conditional Invariant Experience Replay (CIER)} that can simultaneously retain old knowledge, acquire new information, and generalize to unseen domains. CIER employs an adversarial training to correct the shift in $P(X,Y)$ by matching $P(X|Y)$, which results in an invariant representation that can generalize to unseen domains during inference. Our extensive experiments show that CIER can bridge the domain gap in continual learning and significantly outperforms state-of-the-art methods. We will release our benchmarks and implementation upon acceptance.