With the continuous development of knowledge graph completion (KGC) technology, the problem of few-shot knowledge graph completion (FKGC) is becoming increasingly prominent. Traditional methods for KGC are not effective in addressing this problem due to the lack of sufficient data samples. Therefore, completing the task of knowledge graph with few-shot data has become an urgent issue that needs to be addressed and solved. This paper first presents a concise introduction to FKGC, which covers relevant definitions and highlights the advantages of FKGC techniques. We then categorize FKGC methods into meta-learning-based, metric-based, and graph neural network-based methods, and analyze the unique characteristics of each model. We also introduced the research on FKGC in a specific domain - Temporal Knowledge Graph Completion (TKGC). Subsequently, we summarized the commonly used datasets and evaluation metrics in existing methods and evaluated the completion performance of different models in TKGC. Finally, we presented the challenges faced by FKGC and provided directions for future research.