Within only a few decades from its initial introduction, the field of surgical robotics has evolved into a dynamic and rapidly growing research area with increasing clinical uptake worldwide. Initially introduced for stereotaxic neurosurgery, surgical robots are now involved in an increasing number of procedures, demonstrating their practical clinical potential while propelling further advances in surgical innovations. Emerging platforms are also able to perform complex interventions through only a single-entry incision, and navigate through natural anatomical pathways in a tethered or wireless fashion. New devices facilitate superhuman dexterity and enable the performance of surgical steps that are otherwise impossible. They also allow seamless integration of microimaging techniques at the cellular level, significantly expanding the capabilities of surgeons. This paper provides an overview of the significant achievements in surgical robotics and identifies the current trends and future research directions of the field in making surgical robots safer, smaller, and smarter.