The premise of this symposium is that the ideas of reinforcement learning have impacted many fields, including artificial intelligence, neuroscience, control theory, psychology, and economics. But what are these ideas and which of them is key? Is it the idea of reward and reward prediction as a way of structuring the problem facing both natural and artificial systems? Is it temporal-difference learning as a sample-based algorithm for approximating dynamic programming? Or is it the idea of learning online, by trial and error, searching to find a way of behaving that might not be known by any human supervisor? Or is it all of these ideas and others, all coming to renewed prominence and significance as these fields focus on the common problem that faces animals, machines, and societies - how to predict and control a hugely complex world that can never be understood incompletely, but only as a gross, ever-changing approximation? In this talk I seek to start the process of phrasing and answering these questions. In some cases, from my own experience, I can identify which ideas have been the most important, and guess which will be in the future. For others I can only ask the other speakers and attendees to provide informed perspectives from their own fields.