Fault detection and diagnosis play a crucial role in ensuring the reliability and safety of modern industrial systems. For safety and cost considerations, critical equipment and systems in industrial operations are typically not allowed to operate in severe fault states. Moreover, obtaining labeled samples for fault diagnosis often requires significant human effort. This results in limited labeled data for many application scenarios. Thus, the focus of attention has shifted towards learning from a small amount of data. Few-shot learning has emerged as a solution to this challenge, aiming to develop models that can effectively solve problems with only a few samples. This approach has gained significant traction in various fields, such as computer vision, natural language processing, audio and speech, reinforcement learning, robotics, and data analysis. Surprisingly, despite its wide applicability, there have been limited investigations or reviews on applying few-shot learning to the field of mechanical fault diagnosis. In this paper, we provide a comprehensive review of the relevant work on few-shot learning in mechanical fault diagnosis from 2018 to September 2023. By examining the existing research, we aimed to shed light on the potential of few-shot learning in this domain and offer valuable insights for future research directions.