Recent technological advances in surgery have resulted in the development of a range of new techniques that have reduced patient trauma, shortened hospitalization, and improved diagnostic accuracy and therapeutic outcome. Despite the many appreciated benefits of minimally invasive surgery (MIS) compared to traditional approaches, there are still significant drawbacks associated with conventional MIS including poor instrument control and ergonomics caused by rigid instrumentation and its associated fulcrum effect. The use of robot assistance has helped to realize the full potential of MIS with improved consistency, safety and accuracy. The development of articulated, precision tools to enhance the surgeon's dexterity has evolved in parallel with advances in imaging and human-robot interaction. This has improved hand-eye coordination and manual precision down to micron scales, with the capability of navigating through complex anatomical pathways. In this review paper, clinical requirements and technical challenges related to the design of robotic platforms for flexible access surgery are discussed. Allied technical approaches and engineering challenges related to instrument design, intraoperative guidance, and intelligent human-robot interaction are reviewed. We also highlight emerging designs and research opportunities in the field by assessing the current limitations and open technical challenges for the wider clinical uptake of robotic platforms in MIS.