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Building autonomous machines that can explore open-ended environments, discover possible interactions and build repertoires of skills is a general objective of artificial intelligence. Developmental approaches argue that this can only be achieved by autotelic agents: intrinsically motivated learning agents that can learn to represent, generate, select and solve their own problems. In recent years, the convergence of developmental approaches with deep reinforcement learning (RL) methods has been leading to the emergence of a new field: developmental reinforcement learning. Developmental RL is concerned with the use of deep RL algorithms to tackle a developmental problem— the intrinsically motivated acquisition of open-ended repertoires of skills. The self-generation of goals requires the learning of compact goal encodings as well as their associated goal-achievement functions. This raises new challenges compared to standard RL algorithms originally designed to tackle pre-defined sets of goals using external reward signals. The present paper introduces developmental RL and proposes a computational framework based on goal-conditioned RL to tackle the intrinsically motivated skills acquisition problem. It proceeds to present a typology of the various goal representations used in the literature, before reviewing existing methods to learn to represent and prioritize goals in autonomous systems. We finally close the paper by discussing some open challenges in the quest of intrinsically motivated skills acquisition.