Rolling bearings are critical components that are prone to faults in the operation of rotating equipment. Therefore, it is of utmost importance to accurately diagnose the state of rolling bearings. This review comprehensively discusses classical algorithms for fault diagnosis of rolling bearings based on vibration signal, focusing on three key aspects: data preprocessing, fault feature extraction, and fault feature identification. The main principles, key features, application difficulties, and suitable occasions for various algorithms are thoroughly examined. Additionally, different fault diagnosis methods are reviewed and compared using the Case Western Reserve University (CWRU) bearing dataset. Based on the current research status in bearing fault diagnosis, future development directions are also anticipated. It is expected that this review will serve as a valuable reference for researchers aiming to enhance their understanding and improve the technology of rolling bearing fault diagnosis.