Object detection as a subfield within computer vision has achieved remarkable progress, which aims to accurately identify and locate a specific object from images or videos. Such methods rely on large-scale labeled training samples for each object category to ensure accurate detection, but obtaining extensive annotated data is a labor-intensive and expensive process in many real-world scenarios. To tackle this challenge, researchers have explored few-shot object detection (FSOD) that combines few-shot learning and object detection techniques to rapidly adapt to novel objects with limited annotated samples. This paper presents a comprehensive survey to review the significant advancements in the field of FSOD in recent years and summarize the existing challenges and solutions. Specifically, we first introduce the background and definition of FSOD to emphasize potential value in advancing the field of computer vision. We then propose a novel FSOD taxonomy method and survey the plentifully remarkable FSOD algorithms based on this fact to report a comprehensive overview that facilitates a deeper understanding of the FSOD problem and the development of innovative solutions. Finally, we discuss the advantages and limitations of these algorithms to summarize the challenges, potential research direction, and development trend of object detection in the data scarcity scenario.