Personalized recommendations have become a common feature of modern online services, including most major e-commerce sites, media platforms and social networks. Today, due to their high practical relevance, research in the area of recommender systems is flourishing more than ever. However, with the new application scenarios of recommender systems that we observe today, constantly new challenges arise as well, both in terms of algorithmic requirements and with respect to the evaluation of such systems. In this paper, we first provide an overview of the traditional formulation of the recommendation problem. We then review the classical algorithmic paradigms for item retrieval and ranking and elaborate how such systems can be evaluated. Afterwards, we discuss a number of recent developments in recommender systems research, including research on session-based recommendation, biases in recommender systems, and questions regarding the impact and value of recommender systems in practice.