Projective Simulation (PS) is a model for agency that incorporates aspects of reinforcement learning, an indeterministic basic dynamics inspired by physical hopping processes as studied in quantum optics, and an overall orientation towards agency as a continuous process of interaction with the environment as described by phenomenology. We explain the formal structure of PS in detail and compare it to the more standard paradigm of reinforcement learning. PS stands out mostly due to its specific memory structure (Episodic and Compositional Memory, ECM) and its openness, which makes it apt as an agency model rather than just a learning model: PS does not start from a fixed environment model to be “solved”. The focus is, rather, on the internal dynamics of deliberation, which is resolved as a stochastic process within the ECM, as well as on learning and adaptation over a long time, allowing for significant and even disruptive changes in the environment to be incorporated. After discussing the model, we showcase several applications of PS, prominently in basic research in quantum mechanics and especially in quantum information. This strengthens our claim about the intimate connection between agency and quantum physics that we already defended in Chaps. 3 and 4 . We also consider quantum versions of PS, which promise to show quantum advantages in machine learning while retaining a maximum of transparency. These applications motivate a separate discussion of transparency and traceability in the context of explainable (quantum) AI.