Intrinsic motivation, centrally involved in spontaneous exploration and curiosity, is a crucial concept in developmental psychology. It has been argued to be a crucial mechanism for open-ended cognitive development in humans, and as such has gathered a growing interest from developmental roboticists in the recent years. The goal of this paper is threefold. First, it provides a synthesis of the different approaches of intrinsic motivation in psychology. Second, by interpreting these approaches in a computational reinforcement learning framework, we argue that they are not operational and even sometimes inconsistent. Third, we set the ground for a systematic operational study of intrinsic motivation by presenting a formal typology of possible computational approaches. This typology is partly based on existing computational models, but also presents new ways of conceptualizing intrinsic motivation. We argue that this kind of computational typology might be useful for opening new avenues for research both in psychology and developmental robotics.