An important feature of human learning is the ability to continuously accept new information and unify it with existing knowledge, a process that proceeds largely automatically and without catastrophic side-effects. A generally intelligent machine (AGI) should be able to learn a wide range of tasks in a variety of environments. Knowledge acquisition in partially-known and dynamic task-environments cannot happen all-at-once, and AGI-aspiring systems must thus be capable of cumulative learning: efficiently making use of existing knowledge while learning new things, increasing the scope of ability and knowledge incrementally—without catastrophic forgetting or damaging existing skills. Many aspects of such learning have been addressed in artificial intelligence (AI) research, but relatively few examples of cumulative learning have been demonstrated to date and no generally accepted explicit definition exists of this category of learning. Here we provide a general definition of cumulative learning and describe how it relates to other concepts frequently used in the AI literature.