Incrementally learning new information from a non-stationary stream of data, referred to as ‘continual learning’, is a key feature of natural intelligence, but an open challenge for deep learning. For example, standard deep neural networks tend to catastrophically forget previous tasks or data distributions when trained on a new one. Enabling these networks to incrementally learn, and retain, information from different contexts has become a topic of intense research. In this presentation I put forward the view that there are three fundamental types, or ‘scenarios’, of continual learning: task-incremental, domain-incremental and class-incremental learning. I argue that each of these scenarios has its own set of challenges, and I demonstrate that there are substantial differences between them in terms of difficulty and in terms of the effectiveness of different computational strategies.