This paper presents a comprehensive review of the state-of-the-art techniques for predicting the remaining useful life (RUL) of rolling bearings. Four key aspects of bearing RUL prediction are considered: data acquiring, construction of health indicators (HI), development of RUL prediction algorithms, and evaluation of prediction results. Additionally, publicly available datasets that can be used to validate bearing prediction algorithms are described. The existing RUL prediction algorithms are categorized into three types and have been comprehensively reviewed: physical-based, statistical-based, and data-driven. In particular, the progress made in data-driven prediction methods is summarized, and typical methods such as RNN, TCN, GCN, Transform, and TL-based methods are introduced in detail. Finally, the challenges faced by data-driven methods in RUL prediction for bearings are discussed.