Rotating machinery often works under time-varying speeds, and nonstationary conditions as well as harsh environments make its key parts, such as rolling bearings and gears, prone to faults. Therefore, a number of fault diagnosis methods including nonstationary signal processing methods and data-driven methods have been developed. This paper presents a comprehensive review on the fault diagnosis of rotating machinery under time-varying speeds proposed mainly during the last five years. First, spectrum analysis-based methods, including order tracking, cyclic spectrum correlation and generalized demodulation, are reviewed. Second, the time-frequency analysis (TFA) methods in machinery fault diagnosis are divided into postprocessing methods and chirplet transform-based methods and are reviewed. Then, the artificial feature extraction-and deep learning-enabled intelligent diagnosis methods proposed specifically for time-varying speed conditions are reviewed. Finally, the research prospects are discussed.We not only review the relevant state-of-art methods and analyze how they overcome the problems caused by speed fluctuations but also discuss their advantages and disadvantages as well as the challenges that will be encountered when applying them to industrial applications. This paper is expected to provide new graduate students, institutions and companies with a preliminary understanding of the methods on this topic.