Personalized recommender systems have become indispensable in today's online world. Most of today's recommendation algorithms are data-driven and based on behavioral data. While such systems can produce useful recommendations, they are often uninterpretable, black-box models that do not incorporate the underlying cognitive reasons for user behavior in the algorithms' design. This survey presents a thorough review of the state of the art of recommender systems that leverage psychological constructs and theories to model and predict user behavior and improve the recommendation process - so-called psychology-informed recommender systems. The survey identifies three categories of psychology-informed recommender systems: cognition-inspired, personality-aware, and affect-aware recommender systems. For each category, the authors highlight domains in which psychological theory plays a key role. Further, they discuss selected decision-psychological phenomena that impact the interaction between a user and a recommender. They also focus on related work that investigates the evaluation of recommender systems from the user perspective and highlight user-centric evaluation frameworks, and potential research tasks for future work at the end of this survey.