Wounds not only harm the physical and mental health of patients, but also introduce huge medical costs. Meanwhile, there is a shortage of physicians in some areas, and clinical examinations are sometimes unreliable in wound diagnosis. Reliable wound analysis is of great importance in its diagnosis, treatment, and care. Currently, deep learning has developed rapidly in the field of computer vision and medical imaging and has become the most commonly used technique in wound image analysis. This paper studies the current research on deep learning in the field of wound image analysis, including classification, detection, and segmentation. We first review the publicly available datasets from various research, and study the preprocessing methods used in wound image analysis. Second, various models used in different deep learning tasks (classification, detection, and segmentation) and their applications in different types of wounds (e.g., burns, diabetic foot ulcers, pressure ulcers) are investigated. Finally, we discuss the challenges in the field of wound image analysis using deep learning, and provide an outlook on the research and development prospects.