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Novelty and surprise play significant roles in animal behavior and in attempts to understand the neural mechanisms underlying it. They also play important roles in technology, where detecting observations that are novel or surprising is central to many applications, such as medical diagnosis, text processing, surveillance, and security. Theories of motivation, particularly of intrinsic motivation, place novelty and surprise among the primary factors that arouse interest, motivate exploratory or avoidance behavior, and drive learning. In many of these studies, novelty and surprise are not distinguished from one another: the words are used more-or-less interchangeably. However, while undeniably closely related, novelty and surprise are very different. The purpose of this article is first to highlight the differences between novelty and surprise and to discuss how they are related by presenting an extensive review of mathematical and computational proposals related to them, and then to explore the implications of this for understanding behavioral and neuroscience data. We argue that opportunities for improved understanding of behavior and its neural basis are likely being missed by failing to distinguish between novelty and surprise