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Today's online music services like Spotify provide their listeners with different types of music recommendations, e.g., in the form of weekly recommendations or personalized radio stations. Such recommendations are often based, at least in parts, on collaborative filtering techniques. In this chapter, we first review the different types of music recommendations that can be found in practice and discuss the specific challenges of the domain. Next, we discuss technical approaches for the problems of music discovery and next-track recommendation in more depth, with a specific focus on their practical application at Spotify. Finally, we further elaborate on open challenges in the field and revisit the specific problems of evaluating music recommendation systems in academic environments.