Artificial intelligence (AI) has emerged as a transformative tool in surgery, particularly in telesurgery and telementoring. However, its potential to enhance data transmission efficiency and reliability in these fields remains unclear. While previous reviews have explored the general applications of telesurgery and telementoring in specific surgical contexts, this review uniquely focuses on AI models designed to optimise data transmission and mitigate delays. We conducted a comprehensive literature search on PubMed and IEEE Xplore for studies published in English between 2010 and 2023, focusing on AI-driven, surgery-related, telemedicine, and delay-related research. This review includes methodologies from journals, conferences, and symposiums. Our analysis identified a total of twelve AI studies that focus on optimising network resources, enhancing edge computing, and developing delay-robust predictive applications. Specifically, three studies addressed wireless network resource optimisation, two proposed low-latency control and transfer learning algorithms for edge computing, and seven developed delay-robust applications, five of which focused on motion data, with the remaining two addressing visual and haptic data. These advancements lay the foundation for a truly holistic and context-aware telesurgical experience, significantly transforming remote surgical practice and education. By mapping the current role of AI in addressing delay-related challenges, this review highlights the pressing need for collaborative research to drive the evolution of telesurgery and telementoring in modern robotic surgery.