This review addresses the problem of learning abstract representations of the measurement data in the context of Deep Reinforcement Learning (DRL). While the data are often ambiguous, high-dimensional, and complex to interpret, many dynamical systems can be effectively described by a low-dimensional set of state variables. Discovering these state variables from the data is a crucial aspect for improving the data efficiency, robustness and generalization of DRL methods, tackling the curse of dimensionality, and bringing interpretability and insights into black-box DRL. This review provides a comprehensive and complete overview of unsupervised representation learning in DRL by describing the main Deep Learning tools used for learning representations of the world, providing a systematic view of the method and principles, summarizing applications, benchmarks and evaluation strategies, and discussing open challenges and future directions.