Artificial intelligence (AI) is making significant advances toward becoming a well-established and promise-bearing technology in various medical domains such as screening, diagnostics, and biopharma research. However, its state remains relatively nascent in surgery and surgical therapeutics. This presents an opportunity for leveraging ongoing rapid advances in AI technology and the increasing availability of large, diverse datasets to pave the way for their use in these domains. Expanding the use of AI to include various processes in surgery-related workflows could provide several benefits, such as greater assurance for reduced errors, better assistance to surgeons, and overall improved patient outcomes. To encourage further research in surgical AI, this article summarizes the state-of-the-art in AI assurance in various aspects of a patient's timeline when undergoing head and neck surgeries, including diagnostics, preoperative considerations, intraoperative guidance, and postoperative and outcome predictions. The work aims to highlight gaps in the state-of-the-art and identify opportunities for the computer-based medical systems community to encourage future research and development on the subject.