Continual learning agents experience a stream of (related) tasks. The main challenge is that the agent must not forget previous tasks and also adapt to novel tasks in the stream. We are interested in the intersection of two recent continual-learning scenarios. In meta-continual learning, the model is pre-trained using meta-learning to minimize catastrophic forgetting of previous tasks. In continual-meta learning, the aim is to train agents for faster remembering of previous tasks through adaptation. In their original formulations, both methods have limitations. We stand on their shoulders to propose a more general scenario, OSAKA, where an agent must quickly solve new (out-of-distribution) tasks, while also requiring fast remembering. We show that current continual learning, meta-learning, meta-continual learning, and continual-meta learning techniques fail in this new scenario. We propose Continual-MAML, an online extension of the popular MAML algorithm as a strong baseline for this scenario. We show in an empirical study that Continual-MAML is better suited to the new scenario than the aforementioned methodologies including standard continual learning and meta-learning approaches.