To ensure that researchers are well-informed regarding infrared image edge detection algorithms and to provide a valuable reference for follow-up investigations, we review relevant research conducted on infrared image edge detection algorithms in the past ten years. First, infrared imaging and edge detection technology are summarized, and then, the difficulties and challenges of infrared image edge detection algorithms are described. Finally, the main infrared image edge detection algorithms are summarized, and the related algorithms are divided into four categories: improved classic edge detection operator-based algorithms, ant colony algorithm-based algorithms, mathematical morphology-based algorithms, and network model-based algorithms. Considering traditional infrared image edge detection algorithms, the morphological method has potential because of its simplicity and ease of use; for non-traditional infrared image edge detection algorithms, the method based on deep learning has stronger pertinence, better robustness, and no requirement of designing complex algorithm steps, which brings new development opportunities to infrared image edge detection.