Head and neck surgery is a fine surgical procedure with a complex anatomical space, difficult operation and high risk. Medical image computing (MIC) that enables accurate and reliable preoperative planning is often needed to reduce the operational difficulty of surgery and to improve patient survival. At present, artificial intelligence, especially deep learning, has become an intense focus of research in MIC. In this study, the application of deep learning-based MIC in head and neck surgery is reviewed. Relevant literature was retrieved on the Web of Science database from January 2015 to May 2022, and some papers were selected for review from mainstream journals and conferences, such as IEEE Transactions on Medical Imaging, Medical Image Analysis, Physics in Medicine and Biology, Medical Physics, MICCAI, etc. Among them, 65 references are on automatic segmentation, 15 references on automatic landmark detection, and eight references on automatic registration. In the elaboration of the review, first, an overview of deep learning in MIC is presented. Then, the application of deep learning methods is systematically summarized according to the clinical needs, and generalized into segmentation, landmark detection and registration of head and neck medical images. In segmentation, it is mainly focused on the automatic segmentation of high-risk organs, head and neck tumors, skull structure and teeth, including the analysis of their advantages, differences and shortcomings. In landmark detection, the focus is mainly on the introduction of landmark detection in cephalometric and craniomaxillofacial images, and the analysis of their advantages and disadvantages. In registration, deep learning networks for multimodal image registration of the head and neck are presented. Finally, their shortcomings and future development directions are systematically discussed. The study aims to serve as a reference and guidance for researchers, engineers or doctors engaged in medical image analysis of head and neck surgery.