Few-shot learning (FSL) is a core topic in the domain of machine learning (ML), in which the focus is on the use of small datasets to train the model. In recent years, there have been many important data-driven ML applications for intrusion detection. Despite these great achievements, however, gathering a large amount of reliable data remains expensive and time-consuming, or even impossible. In this regard, FSL has been shown to have advantages in terms of processing small, abnormal data samples in the huge application space of intrusion detection. FSL can improve ML for scarce data at three levels: the data, the model, and the algorithm levels. Previous knowledge plays an important role in all three approaches. Many promising methods such as data enrichment, the graph neural network model, and multitask learning have also been developed. In this paper, we present a comprehensive review of the latest research progress in the area of FSL. We first introduce the theoretical background to ML and FSL and then describe the general features, advantages, and main methods of FSL. FSL methods such as embedded learning, multitask learning, and generative models are applied to intrusion detection to improve the detection accuracy effectively. Then, the application of FSL to intrusion detection is reviewed in detail, including enriching the dataset by extracting intermediate features, using graph embedding and meta-learning methods to improve the model. Finally, the difficulties of this approach and its prospects for development in the field of intrusion detection are identified based on the previous discussion.