Domain adaptation aims at knowledge transfer from a labeled source domain to an unlabeled target domain. Current domain adaptation methods have made substantial advances in adapting discrete domains. However, this can be unrealistic in real-world applications, where target data usually comes in an online and continually evolving manner as small batches, posing challenges to classic domain adaptation paradigm: (1) Mainstream domain adaptation methods are tailored to stationary target domains, and can fail in non-stationary environments. (2) Since the target data arrive online, the agent should also maintain competence on previous target domains, i.e. to adapt without forgetting. To tackle these challenges, we propose a meta-adaptation framework which enables the learner to adapt to continually evolving target domain without catastrophic forgetting. Our framework comprises of two components: a meta-objective of learning representations to adapt to evolving domains, enabling meta-learning for unsupervised domain adaptation; and a meta-adapter for learning to adapt without forgetting, reserving knowledge from previous target data. Experiments validate the effectiveness our method on evolving target domains.