Akin to neuroplasticity in human brains, the plasticity of deep neural networks enables their quick adaption to new data. This makes plasticity particularly crucial for deep Reinforcement Learning (RL) agents: Once plasticity is lost, an agent's performance will inevitably plateau because it cannot improve its policy to account for changes in the data distribution, which are a necessary consequence of its learning process. Thus, developing well-performing and sample-efficient agents hinges on their ability to remain plastic during training. Furthermore, the loss of plasticity can be connected to many other issues plaguing deep RL, such as training instabilities, scaling failures, overestimation bias, and insufficient exploration. With this survey, we aim to provide an overview of the emerging research on plasticity loss for academics and practitioners of deep reinforcement learning. First, we propose a unified definition of plasticity loss based on recent works, relate it to definitions from the literature, and discuss metrics for measuring plasticity loss. Then, we categorize and discuss numerous possible causes of plasticity loss before reviewing currently employed mitigation strategies. Our taxonomy is the first systematic overview of the current state of the field. Lastly, we discuss prevalent issues within the literature, such as a necessity for broader evaluation, and provide recommendations for future research, like gaining a better understanding of an agent's neural activity and behavior.