Species identification and counting are important content of object detection of insects in the field, which is of great significance to the monitoring, early warning and scientific prevention and control of pests. Traditional methods for identifying and counting insect species are inefficient and struggle to address the diverse range of insects encountered in the field, falling short of the demands of intelligent agriculture for effective pest management. However, with the rapid development of computer and internet technology, insect object detection methods have evolved to become increasingly intelligent and precise. In recent years, image-based insect object detection, leveraging its advantages of high efficiency, ease of operation, and wide applicability, has become the primary technical approach for insect species identification and counting both domestically and internationally. This paper reviews the feature extraction techniques and classifiers of traditional object detection algorithms. Furthermore, it describes anchor based deep learning object detection models, such as YOLO (You Only Look Once) series, SSD (Single Shot Multibox Detector) series. Additionally, the paper introduces anchor free deep learning object detection models, such as the CornerNet series. Lastly, it discusses the prevalent challenges and future research directions in the realm of image-based insect object detection.