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The advances of intelligent fault diagnosis in recent years show that deep learning has strong capability of automatic feature extraction and accurate identification for fault signals. Nevertheless, data scarcity and varying working conditions can degrade the performance of the model. More recently, a tool has been proposed to address the above challenges simultaneously. Meta-learning, also known as learning to learn, uses a small sample to quickly adapt to a new task. It has great application potential in few-shot and cross-domain fault diagnosis, and thus has become a promising tool. However, there is a lack of a survey to conclude existing work and look into the future. This paper comprehensively investigates deep meta-learning in fault diagnosis from three views: (i) what to use, (ii) how to use, and (iii) how to develop, i.e. algorithms, applications, and prospects. Algorithms are illustrated by optimization-, metric-, and model-based methods, the applications are concluded in few-shot cross-domain fault diagnosis, and open challenges, as well as prospects, are given to motivate the future work. Additionally, we demonstrate the performance of three approaches on two few-shot cross-domain tasks. Typical meta-learning methods are implemented and available at https://github.com/fyancy/MetaFD. • Review the advances of meta-learning in fault diagnosis for the first time. • Demonstrate deep meta-learning in fault diagnosis via algorithms and applications. • Illuminate meta-learning algorithms by mathematical optimization. • Stimulate future work with open challenges and prospects. [ABSTRACT FROM AUTHOR]