Robotic surgery has become part of the clinical practice and an extensively studied research domain. Extending the traditional concept of image guidance, capsule, continuum, and microrobots and the dominating robot-assisted minimally invasive surgery (RAMIS) systems support the work of the surgeons. The global-scale adoption in the data age brings new challenges to researchers, engineers, ethics professionals, and legal regulatory experts. Even today, commercialized systems are almost exclusively based on human-in-the-loop control or deterministic algorithmic solutions (such as registration techniques for image-guided technologies), and adaptive decision-making expert systems are lagging. Artificial Intelligence (AI) is one of the most studied research areas; learning from big data shows very promising results in the critical parts of surgery, such as vision, decision support, reasoning, diagnostics, and situation awareness. AI can reduce the complexity of intra-operative workflow, provide predictions on patient outcomes, and enhance efficiency in postoperative reporting. AI-based solutions can create a completely new sub-field, dubbed autonomous robotic surgery, where the systems can provide autonomy supported by proper decision-making and problem-solving capabilities. In this chapter, the most significant, already advanced (research prototypes and commercialized) surgical robotic systems (RAMIS, image-guided, cooperative, continuum, micro, and capsule robots) are introduced, along with the domain’s legal and ethical considerations. The most thoroughly studied research topics are introduced based on the current global trends, highlighting the AI-based approaches having the highest possible impact on the clinical practice. Additionally, future trends and challenges to tackle in AI-driven robotic surgery are presented.