Hyperspectral image (HSI) classification is one of the hotspots in remote sensing, and many methods have been continuously proposed in recent years. However, it is still challenging to achieve high accuracy classification in applications. One of the main reasons is the lack of labeled data. Due to the limitation of spatial resolution, manual labeling of HSI data is time-consuming and costly, so it is difficult to obtain a large amount of labeled data. In such a situation, many researchers turn their attention to the study of HSI classification with small samples. Focusing on this topic, this paper provides a systematic review of the research progress in recent years. Specifically, this paper contains three aspects. First, considering that the taxonomy used in previous review articles is not well-developed and confuses the reader, we propose a novel taxonomy based on the form of data utilization. This taxonomy provides a more accurate and comprehensive framework for categorizing the various approaches. Then, using the proposed taxonomy as a guideline, we analyze and summarize the existing methods, especially the latest research results (both deep and non-deep models) that were not included in the previous reviews, so that readers can understand the latest progress more clearly. Finally, we conduct several sets of experiments and present our opinions on current problems and future directions.