Like in many other research areas, deep learning (DL) is increasingly adopted in music recommendation systems (MRS). Deep neural networks are used in this domain particularly for extracting latent factors of music items from audio signals or metadata and for learning sequential patterns of music items (tracks or artists) from music playlists or listening sessions. Latent item factors are commonly integrated into content-based filtering and hybrid MRS, whereas sequence models of music items are used for sequential music recommendation, e.g., automatic playlist continuation. This review article explains particularities of the music domain in RS research. It gives an overview of the state of the art that employs deep learning for music recommendation. The discussion is structured according to the dimensions of neural network type, input data, recommendation approach (content-based filtering, collaborative filtering, or both), and task (standard or sequential music recommendation). In addition, we discuss major challenges faced in MRS, in particular in the context of the current research on deep learning.