© 2019, Springer Nature B.V. In recent years, unsupervised feature selection methods have raised considerable interest in many research areas; this is mainly due to their ability to identify and select relevant features without needing class label information. In this paper, we provide a comprehensive and structured review of the most relevant and recent unsupervised feature selection methods reported in the literature. We present a taxonomy of these methods and describe the main characteristics and the fundamental ideas they are based on. Additionally, we summarized the advantages and disadvantages of the general lines in which we have categorized the methods analyzed in this review. Moreover, an experimental comparison among the most representative methods of each approach is also presented. Finally, we discuss some important open challenges in this research area.